In Light of Good King Moggle Mog maybe we should reconsider if the Primals are infact being summoned or are in fact created again and again by the rituals that summon them.
Lets Look at the Good King's quests and compare. The Scions repeatedly state the Good King disturbs the Aether just like any proper primal. He even seems to cause a tempering like effect in the Moogles who summon him. For all intents and purposes he is a Primal.
Yet its also made clear that he isn't being drawn down from Heaven(or beyond the grave) but rather is a story given real existence by act of the dark ritual. So my thought is, what if the same is true of the Primals? That the Ifrit worth being worship has a separate existence from the monster that is "summoned"(or may not exist at all), that the ritual creates something new from the passionate memories and faith of the tribe.
My only real problem with this thesis is that Ifrit knew of the Echo, and that would seem to be knowledge his faithful lacked. Secondly when they were bound in the Ultima weapon the three primals were unable to be summoned/Of course this might be a factor of the beast tribes knowing they are bound and thus believing they cannot be summoned. On the otherhand how would they know such things readily?