The run ends on the final hit of Master Hand as soon as soon as the hit occurs, regardless of when you end your splits. Most runners have a final split on the last hit. A couple of runners (me included) have an end split at the end of the credits, but the time of the run is still the moment the last hit on Master Hand occurs. So when you choose to have the last split is up to personal preference, and doesn't affect the end result of the run.
It's the same thing for splitting between each stage. Most runners split as soon as "GAME SET!" shows up on the screen, while a couple runners (again, me included, I'm a rebel Kappa ) split as soon as the announcer screen starts for the next character. It's all personal preference on when you wish to split.
In the end, while everyone has splits set up a different way, time always starts as soon as you press start on the character select screen, and ends the moment the last hit on Master Hand occurs. The way splits are set up within that is entirely up to personal preference
