The Supervisor is incorrect -- Not only do you owe this person OT -- but you'll need to calculate that overtime rate by averaging their pay per hour to calculate the appropriate OT rate. For example. If she works 30 hours at $15/hour and the works at the second job at $10/hour for 20hours -- the OT rate would be (30 x $15) + (20 x $10)/50 hours x 1.5 to get the OT rate.
I would also question the Exempt status of your first employee. Make sure that once you calculate in the 2nd employment that they aren't losing their exemption by working more hours in a non-supervisory role than they should.
We prohibit associates from working more than one job for our company -- it's too difficult to monitor -- and the different divisions don't want to be stuck with the OT costs.
Good Luck