In Vālmīki Rāmāyaṇa (Ayodhyā kāṇḍa), Sri Rāma instructs Lakṣmaṇa to gift dasis to brahmins studying Tattiriya (school of Yajurveda).
kausalyām ca yāaśīrbhir bhaktaḥ paryupatiṣṭhati |
ācāryaḥ taittirīyāṇām abhirūpaḥ ca vedavit || 2-32-15
tasya yānam ca dāsīḥ ca saumitre sampradāpaya |
kauśeyāni ca vastrāṇi yāvat tuṣyati sa dvijaḥ || 2-32-16
"Oh, Lakshmana! Which brahman is studying Taittiriya(a school of yajurveda), a preceptor, a man of conformity; a knower of Vedas, serving Kausalya with his devotion and blessing, to him see that he is duly gifted conveyance, servant maids and silken clothing till he gets satisfied."
But as seen in answers here and here , Taittiriya was first taught by sage Vaisampayana to Yagnavalkya, Subsequently Vaisampayana being offended with Yaganavalkya, made him disgorge the Veda committed to him ; whereupon other disciples of Vaisampayana being commanded to pick it up, took in the form of patridges, and swallowed the soiled texts, hence named black(called Krishna Yajurveda) the other name of Taittiriya referring to the partridges. The said incident has taken place sometime in 28th Dwapara Yuga because Vaisampayana was disciple of Veda Vyasa who was born at time of Mahabharata
But from scriptures we know that Valmikiji composed Ramayana in 24th Treta Yuga. So question is how come Valmikiji use the word Taittiriya to refer to the said Veda when arguably the said incident from which the Veda got the name had not taken place until 28th Dwapar Yuga ?
Please note I am looking for answers based on traditional understanding (ideally backed by scriptures).