I haven't seen anything like that. Tried a Gang War Quick Battle just to be sure, and there was only one red bar filling up. And when it was full, the civvie gangsters got their lime bar, and then it was X-Com again.
I don't recall something like that from my experience with debug mode, either.
Are you perhaps using BOXCE?
Edit: Tried the first turn of QB Gang War with debug mode, and no phases there, either. Most of the gangers took their turns in order, although some delayed part of their turn to later on. Higher ranks seemed to move later, but not exclusively so.
So, I'm not sure where you got that idea. Do you have evidence to support it? Or am I misunderstanding what you're saying?