The important thing to remember there is that primals... aren't natural beings. They are the beliefs and wishes of mortals made physically manifest; they exist only due to mortal desire, so unless summoned in the first place they don't exist at all. This is what makes the only theoretical way to permanently kill a primal wiping out all traces of its memory - as long as someone remembers a primal (or myths surrounding it) it should still exist in the aetherial plane. Their entropic nature and immaterial existence is precisely what makes stopping the primal threat for good nigh-impossible.

It's lightly implied that primals are twisted into something advantageous to the Ascians' goals - at least when it comes to summons carried out using the Ascian-taught ritual, which most are. Primals summoned by Echo users who Incarnate Summon are naturally exempt from this, but so too is Louisoix, who became Phoenix due to the fervent prayers of Eorzeans and the massive amount of aether drawn for re-sealing Bahamut.