Bhagavata Purana mentions that Bhagavan initially takes the form of Purusa for material creation.
jagṛhe pauruṣaṁ rūpaṁ bhagavān mahad-ādibhiḥ sambhūtaṁ
ṣoḍaśa-kalam ādau loka-sisṛkṣayā
Sūta said: In the beginning of the creation, the Lord first expanded
Himself in the universal form of the puruṣa incarnation and manifested
all the ingredients for the material creation. And thus at first there
was the creation of the sixteen principles of material action. This
was for the purpose of creating the material universes.
The Purusa avatars are the ones associated with the function of creations and the material world.
The three Purusas are described in Satvata Tantra: Patala 1, Verse 30:
viṣṇos tu trīṇi rūpāṇi puruṣākhyāny atho viduḥ | prathamaṁ mahataḥ
sraṣṭṛ dvitīyaṁ tv aṇḍa-saṁsthitam | tṛtīyaṁ sarva-bhūta-sthaṁ tāni
"Scholars know Visnu's three forms, which are called Purusa. The first
one is the creator of Mahat. The second one is in the cosmic egg. The
third one is in all beings. Knowing them, one is liberated in a
The names Karanokadakasyi, Garbhodakasayi, Kshirodakasayi are given to the three purusas based on the functions/location of the three purusas.
Some are of the opinion that these three purusas and the Satvata Tantra are only accepted by Gaudiya Vaishnavas, but that is not correct.
Sridhara Svami quotes the above verse from Satvata Tantra in his commentary on Bhagavata Purana to the verses 3.5.27 and 3.20.12. Vallabhacharya also quotes the verse in commentary to the verse 1.3.1.