In the ones I did the time starts when you gain control of the character and ends when the control stops, which is usually after you pick the guilty person and what to do with them (first case is an exception as the final cutscene requires you to click on a single dialogue option so I counted it in as it's technically an action from the player)

Is it possible to add a category for each case of the game? I never got to running the full game, but have runs for each of the six cases separately and always thought these would be nice sub-categories to have :)