Evaporative cooling trades the enthalpy of a liquid to transition to it to a gaseous phase, lowering the temperature (this doesn't break the 2nd law of thermodynamics because gases have more entropy / are more chaotic / are less orderly than liquids). Which would increase the pressure. Any change in pressure would be short lived; flexible, leaky containers like a tent make for terrible pressure vessels, and there's miles of air above them weighing down on them. I don't get the impression that technical details are this series' strong point, much as it may want them to be.