Well, on the old adiabatic expansion, air gets colder, which increases RH, and at the same time the lower pressure reduces RH. Of the two effects, the temp effect is dominant, so reducing pressure eventually leads to condensation.
Think explosive decompression, so graphically demonstated in the movies. Bang, and cabin fills with fog! Also think dew point at height, which is a lower temp than at the surface for the same balloon of air as it rises, expands in the low pressure and cools. Notwithstanding this, the temp drop quickly catches up and cloud forms.
Also the vortex trails you see from wingtips etc, which is water condensing out in the low pressure at the vortex centre
Dick W