2.4 Aftermath and speculation for future content (Spoilers)

[lololink]

Iceheart isn't in control of Shiva once she completed the summoning, it's Shiva talking, not Ysayle. As for Zodiark we don't know exactly why they can't summon him directly, we don't know if he is the dark crystal ( as he is the zodiac symbol of the serpent and made a previous appearance in the Ivalice games ) or just a very powerful Primal. Truth is that we don't know anything about Zodiark or the Ascians. Maybe it's because Hydaelyn trapped Zodiark or locked him away, it seems that they try to weaken Hydaelyn, by telling to the beastmen to summon their primals ( and even other people, like the little Ala Migho guys that tried to summon Rhalgr ) and sucking the aether out of the planet. At this point we can merely speculate.

[Exodus-E]

Iceheart isn't in control of Shiva once she completed the summoning, it's Shiva talking, not Ysayle.

The Scions speculate that Iceheart may (or may have not) have been in control of Shiva once the latter was summoned.

Personally, I agree with Urianger's assessment in that Iceheart may have simply been "groomed for the role" (and as such, rather than being simply taken over by Shiva, both their minds/souls worked in unison, given they had the exact same ideals, morality, etc.).