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.