What makes you say the tank is pressurized? It sounds like your only evidence is a slight dome in the tank. That could be its natural condition ... particularly with summer heat. If you fill the tank nearly to the top with the inspection port closed, you should be able to hear a release of air by cracking open the inspection port if the tank is pressurized. If you don't detect any air escaping, it's not pressurized.
Also, if you have a feed to the pump from 2 separate tanks, you should close the valve to one tank and only draw from the other. For best practice, draw from just one tank at a time. I can't really follow what you were saying, but it sounds like you are connecting the 2 tanks and the water levels are merely equalizing. If this is what you are doing, you shouldn't. The pump doesn't work very well that way. I don't really know the explanation but I'm pretty sure that you are simply doubling friction losses in the feed lines when you leave both tanks open when pumping water. That has a bad effect on the pump and it pumps water less efficiently.