No, that's only half right. The terrestrial avatars are bound to Vana'diel in its current state, if it changes in some dramatic way - like, say, an apocalypse caused by Promathia being freed and... something something Emptiness, I forget what his actual endgame was but it obviously involved destroying the mothercrystals? - then they revert to mindless beasts, yes.
But the six in the protocrystals aren't terrestrials. They're tied more to the greater FFXI universe than the present Vana'diel we are familiar with; when their version of the world ceased to be, they didn't lose their divinity, they just went to sleep. From The Moonlit Path:
If anything, Promathia winning might have awakened the celestial avatars to wield their power over the world as gods again; might have been neat to have that as a set of bosses in there, and it could have made sense, but instead we got "sure, whatever, people want to punch discount Titan right in the loincloth to get amber light, right?"Carbuncle: Fenrir is, just as we are, one of the new energies born to the world of Vana'diel.
Carbuncle: We new powers are a part of Vana'diel. We must abide by its rules, and can die just like any other beast.
Carbuncle: The "avatars," on the other hand, are lifeforces that belong to an ancient order of things.
Carbuncle: As the ancient past of Vana'diel now sleeps, the lifeforces of the avatars are bound in torpor.
That we can have a discussion like this is a testament to what can be built when you set out your lore and are consistent with it. We know what a terrestrial avatar is, we know what its rules are, we know how it is like and how it is unlike a celestial avatar, and we know how they fit in with the world. Playing too loose with things can just make it a game of "well okay, guess we're doing this now".