Hey! Nice concept.
About the 'warp back' timer: I think it would make more sense if the timer was more like the one in Majora's Mask. The player is stuck in a loop that ends with an apocalypse, and he has to stop it. Now, I don't quite understand why is there even a time limit if the player has a time machine)
I liked the idea of having to discover how to stop an apocalypse. One thing though - it would be nice if your past tries had more sense and you didn' have to do the exact same thing every time. It feels like the player's character just loses his memory every time he travels time. For example, there is a contract for Leo, which is marked as 'trash' before you talk to Po. However, next time the player travels time he remembers that this paper is not just trash, but the character seems to not remember that, which is kinda weird) What I'm trying to tell is - it would be great and even more fun if the knowledge you got in the past time travels could be used in the present time travel. Hope you get what I mean)
Overall, nice game and interesting idea!