I agree with what they meant by Carbuncle being Arcanist only they simply meant summoning Carbuncle won't be a cross class skill. Like when looking at this wiki here it says Cura and Curaga require Conjurer, but that doesn't mean White Mage doesn't have access to those skills.

If quests end up being necessary to obtain the other avatars I don't imagine they would have people fight the primals themselves. At most I imagine we would fight the same lesser essence beings that we would be summoning.