Well to summon a primal is faith and aether right? What if the dragons have their own version of Shiva to summon? The one we fought was what Iceheart wished for but the dragons could have their own interpretation made manifest my the right ritual. If Shiva was a historical figure they might actually even remember her mortal form. I think it could be a cool story implication if we had two different versions of the same primal- it's already a big deal that Shiva was summoned in the fashion she was.

I also wouldn't be surprised if Ascians were playing both sides in the war in Ishgard, and manipulated a very young dragon that had not the wisdom of his elders into taking their advice on summoning rituals.