The way that influence switching works is mysterious to me, largely because I've seen it explained several times, all of which contradict each other. Basically, there is a chance to get it switch once the other empire has 4X the influence, but it's random and effected by both how much influence the other empire has, and what the approval rating of the planet is.
The approval rating thing might help explain both those planets, since they are both very happy.
But I agree that the Mind Control Center seems to not do much. Unfortunately, the description isn't specific as to what it does, and since the mechanics of switching are so opaque, I have no idea if it's broken or just useless.