Thanks for filling in the details. Just to be sure I'm understanding this right, when DMX is present everything works properly. When you lose DMX signal the three units go into auto mode except for that the first UFO isn't acting right, and then when you unplug the Quad Phase both UFOs work properly in auto mode? I have a few more questions/suggestions:
-Do all three lights function properly in auto mode when not plugged into any DMX chain (i.e. unplug all your XLR/DMX cables - do the lights run in auto okay)?
-What happens if you move the Quad Phase to the first or last unit in your chain? Set it up both ways and see what happens when you add/remove DMX and Quad Phase power.
-What happens if you keep the chain set up how you've had it , complete with DMX running, and unplug only the Quad Phase?
-When you say 'lose DMX', do you mean you turn off your console, or in your case close the MyDMX software, or are you physically unplugging the XLR/DMX cable from your interface? Try both and see what happens.
As you can see it's pretty much a trial-and-error thing to isolate the problem. To answer your question, no, nothing special should ever happen to the first, last, or for that matter any light in the DMX chain. The order you plug your lights in shouldn't make any difference, but as I mentioned before there are some lights even in the professional market that don't play nicely with others.
My thoughts right now are the either the Quad Phase or DMX interface is doing something weird. Switching the two UFOs around seems to imply that the UFOs physically are not the problem. Another thought - do any of the lights have master/slave mode? If you lose DMX, one or more of the lights might be switching into auto mode with master/slave enabled. Having a mismatch amongst them can definitely cause this problem. The units' manuals will tell you how to enable/disable this and with the digital menus versus the old DIP switches it's very easy to accidentally have this enabled and never even know it.
Give these suggestions a try when you get some time and let me know what happens!