If I were the manager of this supervisor, I would fire them, either that or give them a little more training because their behavior is totally unacceptable.
If an employee is given an unpaid lunch hour, there should be no expectation of them working through their lunch hour. The supervisor is constantly reporting that they work extra time and they work through their lunch hour, but that should not be the expectation of the staff.
The staff is being paid, they have an agreement obviously, from this employee. They’re told that their expectation is to put in a 40 hour work week to expect any more routinely is totally unacceptable.

