It's because Vyasa and Jaimini were working together. Vyasa and two of his disciples, Jaimini and Kasakritsna, together composed a unified work called the Mimamsa Shastra, designed to analyze the meaning of the Vedas in all its aspects. It consisted of 20 Adhyayas or chapters: the 12 Adhyayas of Jaimini's Purva Mimamsa Sutras, analyzing the Karma Kanda of the Vedas (i.e. the Brahmanas and Aranyakas); the 4 Adhyayas of Kasakritsna's now-lost Devata Kanda Sutras, analyzing the Devata Kanda of the Vedas (i.e. the Samhitas); and the 4 Adhyayas of Vyasa's Brahma Sutras, analyzing the Jnana Kanda of the Vedas (i.e. the Upanishads).
The idea is that a student, after he has learned the Vedas, assumes that Dharma leads to the highest good, and so he studies the Purva Mimamsa Sutras to learn the precise nature of Dharma, especially the performance of Yagnas. But then by studying the Purva Mimamsa Sutras, the student realizes that the fruit of following Dharma is only temporary happiness. So then the student turns to the Devata Kanda, as he assumes that meditating upon the gods leads to the highest good. But the Devata Kanda Sutras reveal that meditating upon ordinary Devas doesn't lead to the highest good. So then the student realizes that Brahman is the only source of eternal happiness (the dharma sukhasyaikantikasya to quote the Gita), and so as the first Sutra of the Brahma Sutras says, "Athato Brahmajijnasa" - "Now therefore there is a desire to know Brahman." Here's what Ramanujacharya says about this Sutra in the Sri Bhashya, his commentary on the Brahma Sutras:
The purport of the entire Sûtra then is as follows: 'Since the fruit of works known through the earlier part of the Mîmâmsâ is limited and non-permanent, and since the fruit of the knowledge of Brahman--which knowledge is to be reached through the latter part of the Mîmâmsâ--is unlimited and permanent; for this reason Brahman is to be known, after the knowledge of works has previously taken place.'--The same meaning is expressed by the Vrittikâra when saying 'after the comprehension of works has taken place there follows the enquiry into Brahman.' And that the enquiry into works and that into Brahman constitute one body of doctrine, he (the Vrittikâra) will declare later on 'this Sârîraka-doctrine is connected with Gaimini's doctrine as contained in sixteen adhyâyas; this proves the two to constitute one body of doctrine.' Hence the earlier and the later Mîmâmsâ are separate only in so far as there is a difference of matter to be taught by each; in the same way as the two halves of the Pûrva Mîmâmsâ-sûtras, consisting of six adhyâyas each, are separate 1; and as each adhyâya is separate. The entire Mîmâmsâ-sâtra--which begins with the Sûtra 'Now therefore the enquiry into religious duty' and concludes with the Sûtra '(From there is) no return on account of scriptural statement'--has, owing to the special character of the contents, a definite order of internal succession. This is as follows. At first the precept 'one is to learn one's own text (svâdhyâya)' enjoins the apprehension of that aggregate of syllables which is called 'Veda,' and is here referred to as 'svâdhyâya.' Next there arises the desire to know of what nature the 'Learning' enjoined is to be, and how it is to be done....
From all these it is understood that the study enjoined has for its result the apprehension of the aggregate of syllables called Veda, on the part of a pupil who has been initiated by a teacher sprung from a good family, leading a virtuous life, and possessing purity of soul; who practises certain special observances and restrictions; and who learns by repeating what is recited by the teacher.... It is further observed that the Veda thus apprehended through reading spontaneously gives rise to the ideas of certain things subserving certain purposes. A person, therefore, who has formed notions of those things immediately, i.e. on the mere apprehension of the text of the Veda through reading, thereupon naturally applies himself to the study of the Mimâmsa, which consists in a methodical discussion of the sentences constituting the text of the Veda, and has for its result the accurate determination of the nature of those things and their different modes. Through this study the student ascertains the character of the injunctions of work which form part of the Veda, and observes that all work leads only to non-permanent results; and as, on the other hand, he immediately becomes aware that the Upanishad sections--which form part of the Veda which he has apprehended through reading--refer to an infinite and permanent result, viz. immortality, he applies himself to the study of the Sârîraka-Mîmâmsâ, which consists in a systematic discussion of the Vedânta-texts, and has for its result the accurate determination of their sense.
The Vrittikara refers to the Vyasa's disciple Baudhayana, whom I discuss in my question here.
In any case, because Vyasa, Jaimini, and Kasakritsna were all composing their respective works simultaneously, they often reference each others' views. That does not mean, however that they always cite each others' views with approval. For instance, in the beginning of Adhyaya 3 Pada 4 of the Brahma Sutras, Vyasa refutes Jaimini's views concerning a fundamental difference between the Purva Mimamsa school, namely the purpose of knowledge of the Atma:
Topic-1: Knowledge not a Subsidiary of Rites
- Badarayana thinks that liberation results from this (knowledge of the Self), (as presented in the Upanishads), because the Vedic texts declare so.
- Jaimini thinks that since the Self holds a subservient position in rites etc., the mention of the result of knowledge is (merely) in glorification of the agent, as is the case elsewhere.
- (This is confirmed) on the strength of what is revealed about the behaviour (of the knowers of Brahman).
- (This is so) because the Upanishad declares this.
- (This is so), because both knowledge and work follow the Self (when it transmigrates).
- (And this is so) because rites are enjoined for one who is possessed of that (knowledge of the Vedas).
- And (this follows) from the restrictive texts.
- But Badarayana’s view stands unshaken because of the instruction that the supreme Self is even greater (than the agent); for so it is revealed (by the Upanishads).
- But the Upanishadic declaration (of conduct) is equally in evidence (proving that knowledge is not subservient to religious acts).
But some references are given with approval. For instance, in Adhyaya 1 Pada 1 Sutra 5 of the Purva Mimamsa Sutras, Jaimini approvingly cites Vyasa's statement that the Vedas are eternal; see this excerpt from Shabara's commentary on the Purva Mimamsa Sutras:
The mention of 'Badarayana' means that 'what is stated here is the opinion of Badarayana'; and the name is mentioned only for showing reverence to Badarayana, and it does not mean that what is stated is not the author's (Jaimini's) opinion.
By the way, on a side note it's rather strange that Jaimini's Purva Mimamsa school has philosophical differences with the Vyasa's Vedanta school, for instance the differences I discuss here and here, when Jaimini was a shishya of Vyasa. That is why I have long suspected that Jaimini did not actually believe the things he was saying. Vyasa may have instructed Jaimini to invent a coherent philosophical system where Dharma is considered the highest good, just so that students will study the system and come away with the conclusion that the fruits of Dharma are temporary and thus Brahman ought to be inquired into. But that's just speculation on my part.
EDIT: I found another reference to the unified nature of the Mimamsa Shastra in this section of Adi Shankaracharya's Brahma Sutra Bhashya. According to Adi Shankaracharya, in Adhyaya 3 Pada 3 Sutra 53 of the Brahma Sutras Vyasa discusses the fact that the soul is different from the body. (Ramanujacharya interprets this Sutra very differently, but that's a subject for another time.) Now a hypothetical opponent objects to this, on the grounds that that the soul being different from the body is already established in the Purva Mimamsa Sutras and thus it is improper for Vyasa to discuss the same subject again. Adi Shankaracharya responds by pointing out that Jaimini himself doesn't actually discuss the soul being different from the body, only Shabara's commentary on Jaimini's Purva Mimamsa Sutras discusses it. So it's perfectly legitimate for Vyasa to discuss it now:
But, an objection is raised, already in the first pâda which stands at the head of this Sâstra (i.e. the first pâda of the Pûrva Mîmâmsâ-sûtras) there has been declared the existence of a Self which is different from the body and hence capable of enjoying the fruits taught by the Sâstra.--True, this has been declared there by the author of the bhâshya, but there is in that place no Sûtra about the existence of the Self. Here, on the other hand, the Sûtrakâra himself establishes the existence of the Self after having disposed of a preliminary objection. And from hence the teacher Sabara Svâmin has taken the matter for his discussion of the point in the chapter treating of the means of right knowledge. For the same reason the reverend Upavarsha remarks in the first tantra--where an opportunity offers itself for the discussion of the existence of the Self--'We will discuss this in the Sârîraka,' and allows the matter to rest there. Here, where we are engaged in an inquiry into the pious meditations which are matter of injunction, a discussion of the existence of the Self is introduced in order to show that the whole Sâstra depends thereon.
This entire argument rests on the premise that the Brahma Sutras are a continuation of the Purva Mimamsa Sutras and thus what is discussed in one shouldn't be repeated in the other.
