The Warrior of Light is not tempered by Hydaelyn.

[Kalise]

What about the beast tribes? Some of them were certainly not tempered, like the Stormblood tribes for obvious reasons, but in particular a couple of the ARR tribes appears unlikely to not have been tempered. I mean the Ixal and Amal'jaa tribes.

I think what might be confusing you is there's a difference between the Beast Tribes actual god and the Primals that the aggressive sects summon.

This was emphasised during Heavensward with the Vanu, where we get assistance with taking out Bismarck because it is clearly not their god, as their god wouldn't go around eating the islands of their home.

Primals are merely simulacrums in the form of whatever idea there is about a particular entity. They're not the ACTUAL entity themselves. This lead to the issue in regards to Bahamut, where the simulacrum went on a rampage and started destroying the world. This lead to Ysayle believing that Shiva was some sort of ice queen. As well as showing why the Beast Tribes we help are not tempered.

Since tempering seems to only happen from Primals, not from the idols who's likeness they are in the form of.

Suggesting that at one point, there may have been an actual Garuda, Ifrit, Leviathan, Ramuh etc. Just like there was an actual Shiva. Thus the tribes knowing about them. But the Primals are a separate entity that only care about draining aether and tempering people to serve them.

In addition, it's also possible that, just like in the case of Shiva, that the original entity was not at all some grandiose powerful being and was instead someone much more normal. Just with time and idolization elevating their status to create the ideas that now take the form of the Primals. Which is the case for Garuda, whom was an Allagan general in charge of the Ixalion units (Whom where the successful creations of the Ixal, whom had wings. Since the species was created by the Allagans, with the Ixali being failures)

[Iscah]

the Ixalion units (Whom where the successful creations of the Ixal, whom had wings. Since the species was created by the Allagans, with the Ixali being failures)

My understanding is that the Ixal are descendants of the Allagan Ixalions, rather than rejects, and lost their wings to evolution since that time.