not sure
9.1 psi is the maximum differential pressure. How your questioner got to 390 instead of 310 isn't specified so I'd elect for the maximum differential pressure and not what you think the programme should do.
As for the rest I'm not sure what you mean at all. Suppose you are at FL390 the outside air pressure is 2.85psi. If the differential pressure is 9.1psi then the cabin pressure is 11.95psi and that according to my calculator is near enough 5,600ft.
Too high a differential pressure is not good for aircraft cycles whichever way you look at it.
Incidentally at 8000ft pressure altitude your cabin gauge should read 10.92psi so if your manual advises an 8.35psi differential for a properly conducted flight with no faults that means the outside pressure can go as low as 2.57psi or 41200 pressure altitude.