Shouldn't your fuel tank vent take care of the pressure? I've never had pressure in any of the dozens of saws I've owned. They bounce around on 4 wheelers, tractors, In carts traveling 5-6 miles out into the woods. No pressure ever. This surprises me. Maybe check your vents.
Neither saw has a primer bulb.
I believe it has to do with the fuel sloshing around in the tank and creating pressure. Almost all engines other than chainsaws have vented gas caps, Saws don't.