If the af-on button is release, then it will always fire as in the video.
However, if I keep the button pressed it will only fire once the green dot has been shown (in af-s) or is showing (in af-c). Except in the circumstances I described above.
I interpret it as follows: as long as I keep the af-on pressed, I tell the camera "keep trying to acquire focus and fire only when this is achieved". Once I release the af-on button, I am telling the camera that I don't require autofocus anymore.