What is times up ? It means you have a amount of time, and you need to finish the things in the time, if you did not finish you have to stop, also if you do anythings after times up, then you are cheeting.
Another type of times up is for the school, the student have the break time to relax, but when the time is over you need to go to next class to wait for the teacher, not the teacher waiting for you.
Times up is a things that help you to know are you late or do the things behind, did not follow on the role.