Go back to HF and get one of their adjustable pressure regulators with the gauge on it. Then put one of their red "pumpkin" water trap filters on after that. Will run you under $10 for both. Then you can use whatever adapter you need to hook in your airbrush hose. Use the adjustable to tweak pressure to your needs. I put the adjustable regulator on a quick disconnect so I can use it at the shop where I work, as well as on the compressor at home(3 gal pancake HF). I can even hook a 25 foot regular hose and disconnect to it and keep the compressor on the porch and use the AB inside.
Compressors turn on and off due to the pressure switch on the compressor, they have a low and high limit setting. You will also have a safety valve "pop-off" that keeps the thing from building too much pressure in the event the pressure switch goes outhose mouse. Talking about regular compressors now, not the little AB types.