No, your school admin. shouldn't be able to see what you are doing on your personal account while you are using their device. As long as your login information remains private, so too should be your online activity here at WyzAnt. Just make sure that you log out of all of WyzAnt's windows before you return your school admin.'s device to them afterwards.
Word of advice though: use your own device as much as possible, just to be sure of the above information. :)