Turn on and off well, water pressure goes up drastically
Check the pressure switch that cycles your pump on and off, it may be malfunctioning. 

So you are using water and the pressure is dropping/low; the pressure switch should sense the pressure drop and kick on the pump, which would fill the tank (compressing the air in the tank) and cause a steady rise in pressure. In theory, when all system components are working correctly, you should never see drastic rise or drop of pressure. 

It sounds like maybe the pressure switch did not kick the pump on at the appropriate setpoint. When you shut the system down entirely and the pressure dropped way low, the switch activated and the pump kicked on.

There are other things it could be I guess (like an electrical malfunction or pressure tank problem of some sort).