According to the Auran Empire Primer, Argollëan is descended from the Proto-Danean language. But reading the history of the setting, it would seem like the Daneans brought their languages south of the Jutting Mountains after elves had already been living in Argollë for who knows how long. So the question is, what language did the elves speak before the Argodaneans settled in their vicinity?
Proto-Danean is the language of the north, and was taught to those peoples by the Faravahar (angelic lawful beings) before the Day Without Night.
In other words, the elves didn’t start to speak Proto-Danean because the Daneans settled near them; rather, they were among the Proto-Danean peoples who learned it from the predecessor civilization.
The Proto-Danean language is the Auran equivalent of Indo-European. As far as the migration timing – consider the following. In the real world, both the Celts and Germans speak Indo-European languages. The Celts reached England around 600 BC. The Germans reached England around 400 AD, almost 1000 years later. The same thing is true in the Auran Empire setting. The elves arrived first, speaking the equivalent of Celtic. Later waves arrived with the equivalent of other tongues, but all related to the same ur-language.