Inside the can is gas under high enough pressure to be liquid. When it is released it becomes gaseous because it is no longer under pressure. The law says that an input of energy is necessary to convert matter from liquid to gaseous form, so it has to suck this energy from its surroundings (someone will object to the word "suck").

This is exactly how a fridge works.

I would hope that a dust buster can is just compressed air or compressed nitrogen, which would be gaseous at room temperature however high the pressure. Deodorants and domestic sprays tend to use butane as a solvent/propellant, and this is liquid in the can. However, I would not spray this near electrical equipment - it is highly inflammable and sprays liquid droplets.

Evaporating liquids to gases (phase change) requires a lot of heat to compensate for breaking the molecular bonds in the liquid: this heat does not raise the temperature and is therefore called latent heat. I don't have data for this, but I think with butane propellant, the gas in the can is used to pressurise the liquid from the top, and the liquid escapes through a tube from the bottom to the button. If the butane just evaporated out of the button, it would not pick up the payload (paint, scent, etc) - this is why it you have to keep it upright. The amount of heat absorbed inside the can is very small - enough to make the gas needed to replace the ejected liquid. The main effect of evaporation is to chill the liquid jet issuing from the can, not the can itself.

With compressed gas cans, the energy needed to eject the gas is absorbed directly from the gas inside the can in accordance with the Gas Laws, which reduces the temperature of the can, not just the ejected material. This is nothing to do with phase changes. Essentially, this is the reverse of the process when the can was filled, when the gas was heated by compression and had to be cooled to ambient temperature. But it seems a gas propellent will freeze the can much more readily than a liquid propellant.