My personal feeling was that there were more ELves in the CAS, but the wealthier ones bugged out when Tir na Nog opened up, then there was a second exodus when Tir Taingire was created... each one drew Elves out of the CAS, which was openly racist. Quite a few other metas also left, but the ELves were wealthier, so more of them made it out.
As far as I know, Tir na nOg never engaged into a policy of welcoming all foreign elves. When Liam O'Connor became prime minister and changed the "description of the state" (as they put it) from "Republic of Ireland" to "Tir na nOg" in 2034, he initiated a rather nationalist policy. Ireland did have as much as 40% of elven birth after the Awakening. So the idea was, elves were a major part of the Irish identity, but not the other way round. Unlike Tir Tairngire, I'm not sure Tir na nOg ever claimed to be an "elven nation". They were far more subtle. On the other hand, there probably was a significant elven immigration nonetheless, just for the fact that elves from other countries would think Tir na nOg would be a nicer place to live for them because elves are not a minority there. Elves born on the continent and moving to Tir na nOg with no knowledge of Gaelic or Sperethiel and the Celtic heritage may be disappointed (well, it could be worse: think about an
English elve trying to settle in Tir na nOg...).
The founders of Tir Tairngire had the Salish-Shidhe government opening its border to metahumans as early as 2029, six years before the secession. The whole point was to have a strong elven population in the area before making their move. It worth noting there was only a very small number of elven birth before 2011. By the time Tir Tairngire was established, the vast majority of its elven population would have been under 25 (if you ask me, the authors made a msitake by setting Tir Tairngire establishment date so early in the timeline). Maybe some came with their human parents, but otherwise, people rarely qualify as "wealthy" at such a young age.