The reason you are hearing the pump is because you have tightened the nyloc nuts for the compressor too much and are crushing the little rubber mounts which the compressor has. The nyloc nuts need to be tightened to around 1.5nm to 2.0nm. This doesnt sound like its very tight but thats why you have the nyloc nuts, so they dont come undone. Loosen off the nuts a little and then try sitting in the vehicle again and see if you can hear the pump then.
You dont say exactly when the compressor keeps pumping. If you have a door open and then check out the compressor is it reguarly cycling then?? If so you may have a leak, if it isnt then you are pretty ok with the fact you dont have a leak in the tank or in the line to it.
Its normal for it to cycle on and off when driving as the suspension system makes constant adjustments to keep the vehicle level.
How often is it cycling on and off?? You may have a slightly leaky bag or a valve block that could do with an o-ring kit.
-Wills