There is no reason that priming the pump should affect the pressure setting.
The pressure setting is done with a small nut on the pressure switch that you see when you take the cover off the switch. Clockwise looking at the nut increases the pressure setting. With dexterity and care, you can set the switch with a wrench or pair of pliers without getting electrocuted. I suggest turning the power off at the circuit breaker.
While you are at it, check the air pressure in your bladder tank. There is usually a fitting on the top of the tank (end if a horizontal tank) that looks like the place you put air in your tire. When the pump is shut off, put a tire gauge on it and check the air pressure. If they are the same, great. If not, the gauges are not reading the same, so make a note of the two readings.
If the difference is great, it may be that the gauge on your pump is bad, which is a possible reason for variations in apparent switch points. Be sure the gauge is correct before you try setting the pressure switch or you will go crazy trying to set it. If you install a new gauge, run the pump until it shuts off. Check the air pressure again. There is an adjustment for setting the differential to make it different from 20 psi (a nut closer to the base of the switch) but I suggest you leave that alone for now.
When you are sure the gauge is correct, or you have a new gauge that you trust, drain all of the water out of the tank by turning off the pump power and slowly draining all the water. Watch/listen when the switch actuates to try to turn on the pump. Is that the pressure where you want the pump to turn on?
After the water stops flowing (the tank will be empty), check the air pressure again. The air pressure in the tank should be about 2 psi LESS than the pressure that you want the pump to start pumping (the ON setting).
If the pressure is too low, you should add air with a compressor (the easy way) or bicycle pump (the hard way).
If the pressure is higher than 2 PSI less than the SWITCH ON point, you have two choices. Increase the on point by adjusting the switch, or vent some air out of the tank. If the air pressure is 38 psi or less, and your pump is capable of 60 psi, I would increase the switch setting to 40/60; but that is your choice. If the pump has marginal at that pressure, then bleed the tank to 28 psi for a 30/50 setting.