Can the TSA require supplemental screening AFTER a flight has landed?
TSA staff actually have very little authority - they can prevent you boarding an airplane, they can stop the airplane from leaving. For everything else, they call the local police (the phone is their Big Stick - they can call in some serious assistance, like SWAT or some loaded F-22s).

This sounds like a classic bureaucratic whoopsie - someone missed the initial screening note, someone else noticed that the box wasn't ticked in the system, and protecting the monthly performance statistics prevailed over common sense. Since the passenger declined the search they can prevent said passenger from boarding a flight, but since he did not wish to board a flight (and has not done anything illegal) all they can do is ask him to leave the secure area. As that is exactly what the passenger wanted to do anyway.....