Why are there pixies, etc. on the First but not the Source?

[Kuroka]

While there are some beast tribes that exist only on the First, there are also tribes that exist only on the Source.

Other than the Pixies, the Source also doesn't have Nu Mou, nor do they have Amaro (which technically are their own tribe with those that regained intelligence).
On the other hand the First doesn't have Sylphs, Namazu, Ananta, Kojin, Vath, Vanu Vanu and even Moogles. Some of these I'm guessing existed before the Flood but there is no way to know which ones. Maybe they even had other beast tribes that don't exist in on the Source but those were also wiped by the Flood.

So Pixies are probably their own thing that only appeared on the First due to whatever made them come to be, same with Nu Mou and Amaro.

Amaro are made by the Ronka mages, before they basically were just animals. No mou could be still out thereor just died out, we cant tell yet...

Sylphs might be the same then pixies, we know they dont give birth like we others do, so it might very well possible they are just the same as pixies, just evolved different due our calamitys and less light aether.

As said by others there are Moogle and those who did the Qitari beast tribe learned they encountered namazu - dont forget their native region just as the Ananta was amont the places destroyed by the light...

The Ananta are a native tribe of the saurce as well, its mentioned they were the base of the allagan Lamia...
Though we do know the Ixal are artificial made... as well might be Vanu and gnah, but they might have just evolved randomly as well.

Given that the Fae of the first can go between worlds trivially, they could pick to be anywhere, but choose the first. Maybe they actually thrive on the high light aether concentration?

They can only after making a contract with us, someone whos aether they can trail there. As she explained they basically become a extension of us, thus allowing that. Normal creatures cant do that as we cant just take others between the worlds (at least not wit massive magics and tech).