It sounds like Student "A" did not log out of their Maple T.A. session. If Student "B" then sat down at the same computer and typed the Maple T.A. URL in the address bar they would still be logged in as Student "A". This is because the browser keeps cookies for student "A", and on the Maple T.A. side the session for Student "A" is still active. Without logging out, the Maple T.A. session will be active for 30 minutes (by default).
This would be similar to logging into an online banking session and then closing the browser tab/window without hitting the logout button. If you leave your computer, anyone with access to your computer can start the browser (or open another tab), type your online banking URL, and be logged in to your session. It is very imported to log out of web sessions, especially when using a shared computer. If for some reason a user does not want to log out, they should at least clear the cookies.