Sounds like a tire/rim issue rather than a pressure or tube issue. Your tube should not be able to push your tire off the bead. What size tires are you running. 90 psi is not high for road type tires, but is high for mtb type tires.
With the tire deflated, how easy is it to get the tire off? The tire should stay on by itself and not fall off the rim. I don't know how to tell you to check bead on the rim and the tire, but basically, those two parts are what keep the tire on the rim. Also ensure when you do inflate that the tire is seated correctly all the way around. Pump up 10-20 psi, check seating and continue if good. However if not seated properly you would likely have a bump that you would feel while riding.