Are they able to make their own decisions or are they a slave to your conjuration magic?
They are bound and cannot make decisions in that way.
The proof is in the conjuration master quest.
You can summon dremora, creatures definitely capable of speaking, consenting, etc, via "Conjure Dremora Lord" and they have no dialogue, cannot be ordered, and do not act as a follower in skyrim would, even an unwilling one. But, at conjuration 90, in the College, you can get a spell, "Conjure Unbound Dremora", which summons a Dremora that is hostile, can speak, and can change its mind if you threaten it with violence. That dremora, once unsummoned, can then willingly (under duress) go get you a sigil stone, and carries it back with him.
Clearly, there's a distinction here, the unbound version of the spell had no compulsion effect on it. This would be needed since after dismissing the spell, the compulsion ends, so they wouldn't obey.
Logically, if we can make a "Summon Unbound Dremora", we could make a "Summon Unbound Flame Atronach", and that spell would repeatedly summon the same atronach with no compulsion, but the standard version of these spells summons things in a way that prevents consent.