Water or water vapor when checking the air pressure in a bladder type tank means the bladder is broken. In an air over water type tank, the tank is water logged and needs an air charge. You usually only have to drain that type tank and turn the pump on.
Anytime a pump runs when water isn't being used, there is a leak somwhere. Shut off the water just past the pressure tank and if the pump runs, the leak is on the well side of the system. Probably a foot valve or check valve but it can be a fitting or hole/split in the drop pipe or a pitless adapter oring. If the pump doesn't run, then the leak or water use is on the house side and probably a toilet flapper or fill valve. Check and adjust the water level in all toilets to 1" below the fill mark or the top of the overflow tube.
A tank never has anything to do with a pump running constantly or from time to time when no water is being used. Or you'd see the water on the floor around the tank because the tank would be leaking.
Gary
Quality Water Associates