Let me take a stab at it.
Let's say you have your tank at 125 PSI. You then have the regulator set for 40 PSI. After cleaning your airbrush, you crank the regulator down to 15 PSI. The regulator bleeds air off at this point. What it's doing is bleeding air from the 'low side' of the regulator, in other words, the airline from the regulator to the airbrush had 40 PSI in it, when you changed the regulator pressure, the regulator opened it's valve to get the line down to 15 PSI. The 'high side' of the regulator never changed. The auto on-off on the compress should still work just fine.
At least, that is my setup, and what happens with my compressor (and it's an auto on-off too). I can't tell from the picture if that has a tank on it or not.
Dan