In the movie, we see him turning back time but there doesn't seem to be any of the logical consequences of this. He doesn't meet himself, nor does he lose the memory of what happened.
In principle, someone travelling through time could meet themselves in either a stable or unstable time loop. If a loop was cut off, they could even end up duplicating themselves multiple times. None of this seems to happen in the film which indicates that Superman is isolated from the effects of reverse time. While he's in space doing his thing, there isn't another Superman on the ground running backwards.
By the same token, he retains a memory of the events that previously unfolded. This gives us a good confirmation that he is personally insulated from the effects of the time reversal or else his mind would unmake the memories it had previously.