Should I still pay an employee for holidays after he's used all his paid time off?
I am assuming from your question that you are requiring people to save their vacation time to use on what would normally be declared company holidays at most companies. That is unusual; and I hope that all employees understand that they are supposed to be saving their vacation time for holidays.
The Fair Labor Standards Act requires you to pay an exempt employee for the entire week in any work week in which the employee has put in work time. This would not be an exception. It would be different for a non-exempt employee. You would not be required to pay a non-exempt employee for a holiday after s/he’s used all of his/her paid time off as long as you apply this rule consistently.