Two things.

When you run payroll, and have assigned time by class, the employer taxes are already allocated to the appropriate class when the liability is created at the time of payroll. This is what you see when you run the report. When you pay the gummint you are merely paying down a short term liability and if you were to break down the payment itself additionally by class you will double post by class.

The other thing, when you run payroll and assign any hours by class you are assigning GROSS WAGE, which includes ALL employee withholdings and no further action is required.

The end result is whatever you are doing in running those reports AND adjusting the recording of the payments is unnecessary and may even be detrimental to your books - take that recovered timeslot each week and have an extra cup of coffee