1. The precharge on a pressure tank is measured when the tank is empty (water pressure = 0). Measuring the air pressure while there is air in the tank is only for comparing the water pressure gauge and air pressure gauge.
2. If your pressure switch was 20-40 and your precharge was 34, for example, the pump would turn off at 40 or so. When water got used, the tank provided water until the pressure dropped to 35. At that point the pressure dropped quickly to below 20 and the pump turned on. The water pressure then rose quickly to 34. There should have been a blip down on the gauge, and the water flow would have paused for a bit.
3. You can increase the cut on and cut off pressure on a typical switch by turning the bigger nut clockwise. This is for a typical Square-D:
To raise or lower the cut-in and cut-out settings while keeping the
differential between those two settings constant, adjust the range
nut. The range nut is the 3/8-inch nut that adjusts the larger of
the two springs in Models FSG, FYG, FRG, and Type G Pumptrol
switches.
Turn the range nut clockwise to increase the cut-in pressure and
counter-clockwise to lower the cut-in pressure. Three and a half
revolutions of the range nut will change both the cut-in and
cut-out settings by approximately 10 psi.
4. After getting the cutoff up to where you want (or where you can get to), you can then set the precharge with the water pressure = 0. With a submersible, this would typically be 2 psi below the cut-on pressure, but it should be more with a jet pump.