This is a very cool concept. And on the core idea is expended upon in a logical manner.
It's neat having to visualize a level rotated before it actually happens so you know where to stand when it happens.
The visuals and sounds are great as well.
And I love the idea to have debug options in a build for a jam so players can expierence the whole game even if they are stuck on a level.
In my opinion the ability to trigger the next turn early should not be a debug option, though. That should be part of the official game mechanics. It's very good that the timing is lenient in some cases to make sure all players are able to make it but waiting for 10ish seconds slows down the game if you are a faster player.
And the thing that brings down the game the most in my opinion are the platforming controls. While it makes physical sense that you aren't able to control your character mid-jump, it just doesn't feel good to play. In a game like this the platforming should be second nature and not be something that the player has to actively think about. I landed in spikes more times than I would care to admit because I couldn't adjust mid-jump. That paired with having to wait on turns made me skip levels that I otherwise could have easily completed.
Apart from that the controls also felt a bit floaty but not too bad actually.
So yeah, fix the platforming controls and make them a bit tighter, make the ability to trigger the turns a main ability and you got yourself a truly great game.
As it is now it's still a very solid game for a GameJam submission. Great job!