The idea of the past / future only affecting a singular level state is a very cool idea, being a very unique take within all the other rewinding / fast-forwarding games. It was a bit confusing at times on what was going to happen, some visual clarity would help a lot with that, with specific some specific sprites maybe. It took me awhile to know that I had a double-jump, which I think I got from the powerup? Eventually, I did get stuck though and didn't know where to go.
Overall theres a lot of potential here for a nice unique take on the rewinding / fast-forward mechanic, nice job!