I just figured out how to get it to work. After creating the Cue you need to open the Cue Inspector, hit the Edit button and then Hit the Rewind Button in the same Movie that the cue is triggering in the Movie control panel on the right. You should see in the Cue Inspector that when you hit the Rewind Button it creates a "Restart" line (instruction) inside the Cue under that particular movie. This instructs the playhead to move back to the beginning the next time the cue activates. Without this "Restart" line next time the movie is triggered it'll simply play from where the playhead was last (at the end of the movie) and so nothing will happen since the movie is set to "Play Once". If you set the movie to "Loop" it will simply play forever and never move on to the Next Cue. BTW If you click on the "Restart" line in the Cue Inspector you'll see it has an On/Off switch.
Also make sure the the Visual line in the Cue Inspector for the Quad being referenced in the Cue is for the same movie. If it's not you can fix this by clicking on the little arrow in the top left corner of the movie icon.
So essentially when the Cue is triggered it tells the Quad that the Visual element is the movie, to reset the movie's playhead to the beginning and then to play the movie once. Then it moves on to the next Cue.
Hope this helps! Almost drove me nuts trying to figure this out! Very obscure.