"The Dark Side - 2 days ago - removed inappropriate salesman language"
Now THAT was inapropriately meaningless. IF you have the right to edit my posts how about give an HONEST reason not silly nonsense like salesman language that isn't remotely related to anything I wrote.
Two lines were removed. One shows a very touchy editor and the other was silly at best. I have been signing my posts since 2000 on many sites. If that is against the rules here then goodby.
The nozzle is irrelevant to the physics involved. The basics of temperature vs pressure in a gas is simple. The compressed gas, not what is going on in the video many saw before coming here, has a heat content as well as a temperature. Increase the volume of the gas, however it is done, if done rapidly as in the question, and it still has the same heat content but in a larger volume, thus the temperature will drop. Basically the energy is now taking up a larger volume and the energy density is decreased, thus the temperature drops.
That answers the original question.
Many are here though came from a video with an ignorant clown that is saying words with no actual relation to what was going on the video.
He was not spraying a gas in the video, it was a liquid. It was a gas before being compressed into the can, for example the can of compressed 'air' I have next to my PC has 1,1 difloroethane in it. At STP, standard temperature and pressure, its a gas. At the high pressure its at in the can, when full, its a liquid for most of the volume of the can. Its in gas form at the top of the can.
Shake the can a bit and you will detect the sloshing. A mostly empty can will have little of the difloroethane in a liquid state. But at the start its almost all in a liquid state. Spray the can according to the instructions and the gas at the top is released. Turn the can upside down and the diflorethane that is in a liquid state is released. The liquid hits the bottle and then evaporates from the heat of the bottle, drawing off heat in the process of being converted from a liquid to a gas. Same thing that happens with water only much faster.
So the bottle is being cooled by rapid evaporation not by the expansion of a gas. Now the can of compressed gas IS cooled by the expansion and by the evaporation of the gas/liquid in the can.