[his time sheet's indicate that he works at the time he is suppose to be on duty at his primary job. Then he's falsifying his work time at one or both locations.

I am assuming this is not legal, however if anyone could shoot me a link to where I could research this more I would love it. This is a matter for management to deal with. Are you in payroll? I'm guessing you are since you have access to the timesheets. Inform the supervisor's manager of what you've seen on the timecards and then let him or her deal with it.