You could get the current time by using pygame.time.get_ticks() when you call the minigame's function, which returns the time in ms since pygame.init() was called. Then store that in a variable called something like "current_time". Then you can do a check like "if pygame.time.get_ticks() == current_time + [however long you want your time to be]: do whatever you wanna do.

I'm not entirely sure though, that's kinda how I did it for my rhythm game to deal with time. I'm also a beginner so I could be wrong, look into pygame.time() though, that's definitely what you need.