The plug allows gas to flow slowly enough from one chamber to the other for the pressures in the two chambers to be kept roughly constant (but different from each other) by pushing one piston slowly 'inwards' and pulling the other slowly outwards. Thus the volume of the gas in one chamber is reduced to zero, while the volume of gas in the other chamber rises from zero. But (in the classic porous plug experiment) the whole process is fast enough to be essentially adiabatic. Speed is, as they say, of the essence!
For what it's worth, I'd rate "because of the plug the pressure decreases" as thoroughly confusing.
Reversible adiabatic expansion of a gas involves the gas expanding quasi-staically doing work against a piston. The gas can be made to go through the whole sequence of states in reverse by reversing the sequence of forces on the piston (and adding an infinitesimal extra force). This cannot be done with the porous plug experiment.