When the fourth mizukage was controlled, zabuza was still in ninja academy because during that time the mist village was called the blood mist village because of the fourth mizukage's actions while he was controlled. But the thing is, according to naruto databooks, zabuza and obito are of the same age.

When the series began Zabuza was 26, the same age as Kakashi who was also the same age was Obito, but when Zabuza was in the ninja academy and killed all of his classmates he was 9 years old. So that should mean by that time Obito should have been nine years old, but he died when he was 13 years old so he couldn't have controlled the mizukage.

So yeah something's kinda screwed up in the timeline. So maybe it was Madara who controlled the Mizukage because I read a theory in this site I think yesterday saying he may have controlled him by using a zetsu through the use of the tubes in his back or something like that.