Here is a balanced diaphragm style scuba regulator diagram.
Obviously things look a little different, maybe even a little more complicated. Really things work in almost exactly the same way.
At rest here the pressure in the intermediate chamber is greater than the ambient water pressure and the diaphragm balance spring. This is exerting force on the diaphragm to the right and allowing the valve to sit against the HP seat, cutting off the HP air flow from the tank.
When you take a breath through the second stage, again the pressure in the intermediate chamber drops, the ambient pressure and spring push against the diaphragm, which pushes against the valve (in this example to the left) and unseats it allowing HP air to flow in from your tank.
When you stop taking air the pressure rises in the intermediate chamber. That combined with the pressure from the valve balance spring push the valve back into the seat (to the right) cutting off HP air flow.
So you see whether piston or diaphragm type a balanced scuba diving regulator works virtually the same.