If the BANK has a employee that is being garnished and the employee also has a checking account at that same bank, does HR only withhold the maximum percentage from their pay and deposit the balance OR is the bank required to also hold monies that go into the checking account from the employee's payroll?

Depends on the wording in the garnishment.

And understand that attaching wages and attaching accounts are two different processes. An order to do one does not also give you a mandate to do the other.