YES! I use old phone chargers and charging cables constantly for little home projects like this.
That little motor called for 5 volts, and it would have been more work to make a converter for the 12 volt power supply from the mister, so I cut some corners (and wires) and skipped some steps for the sake of time and simplicity ;)
You are resourceful! I go out ans buy stuff. I'd like to learn how to do this kind of thing.