I noticed that the level leaderboards have no rules in them so I'm unsure how I should time the level runs (when to start and when to stop the run's timer)

Rules haven't been written yet, but timer starts when you gain control of your character (in Story levels after you close the game message, in Another Story right after the camera settles down). Stops on the very last hit.

Anyways, I will personally take care of checking the exact time for each run.

I kinda figured that but I wanted to be 100% sure thank you