“Eternality” is a later overinterpretation of a term which, in my opinion, originally did not mean that, and continued not to have eternality as its primary meaning throughout its history.

nitya (as shown by Minoru Hara, JAOS 79.2) is etymologically adjective meaning ‘inherent’. This meaning is completely in harmony with its use in the same semantic field as siddha, autpattika, apauruṣeya and svābhāvika in Vyākaraṇa and Mīmāṃsā, as well as dhruva.*

So, how comes that one starts speaking about temporality in connection with nitya? In my hypothesis, there are three steps:

1. In connection with the Mīmāṃsā vs Nyāya controversy, Mīmāṃsā authors insist on the apauruṣeya aspect of language, whereas Nyāya authors insist on language as pauruṣeya. Since language is pauruṣeya, it is not nitya in the sense of being kṛtaka ‘made up’, ‘artificial’. Thus, once again, nitya is not opposed to ‘temporal’ but to ‘artificial’, once again pointing to an opposition which does not have “eternality” as its primary focus.
2. The Mīmāṃsā vs Nyāya controversy evolved also into a Mīmāṃsā vs Buddhist Epistemology controversy. For Buddhist epistemologists, whatever is kṛtaka is also kṣaṇika. Here temporality comes into the picture. Still, the point is not about “eternality” vs, “temporality”, but rather about “fixed/permanent/ummovable” vs “ephemeral”, as shown by the examples mentioned (mountains and rivers are said to be respectively kūṭastha– and pravāhanitya).
3. Euro-American interpreters are used to the topic of temporality and to the concept of eternality, which plays a big role in the Graeco-Roman and in the Judaeo-Christian worldviews. Thus, they are inclined to interpret concepts in this sense, just like it happens with concepts like “Scripture”, “God”, “letter” and the like, which have been introduced uncritically in the Indian debate.

*Yes, you might find nitya also in connection to anādi ‘beginningless’, which might be interpreted temporally (I rather think it just means “for which no beginning can be proved”). But this is just one among the many terms used in juxtaposition with nitya (see above for several others).

P.S. I recently wrote an article on nitya. You can read the pre-print version here.