The characters can stop time because of science.
When one of them stops time, time stops for all of the others as well. The party uses this for heists, do-gooding, whatever they set out to do.
The first few sessions are sandboxed, letting the party do what they do.
Then they discover they're not alone in the stopped time, and the fact that they know they're not alone not only puts them at risk, it endangers the time stream itself.
A Little Piece and Quiet (Twilight Zone episode)