I know My.Sketchup is in Beta Form, but

It seems my.SketchUp hasn’t been designed to be used in shared user sessions. It uses extensive caching in your browser’s local storage to avoid redownloading the same stuff. When two students use the same account on the computer, but switch their signin of the online account, the browser cache still contains the same models and confuses SketchUp.

To solve the issue, you could clear local storage in the browser’s preferences. I don’t know whether my.SketchUp has a setting not to use local storage.

If you log out of the previous student’s computer account, then log into the second student’s computer account and then sign into the second student’s online account, the issue should not occur.