When does the first rotor in Enigma machine rotate?
Having had the privilege of using one of the original machines, I can tell you the sequence is the following:  set the plugs, and set the rotors.  Once you push the key, you can feel the force of the rotors turn, and the light turns on for the encrypted letter.  The light turn off when you take pressure off the key.

This was on a 3-wheel Enigma, and I do not have any personal experience with the later models, but I will assume they work the same way.