Am I doing something wrong because the order on the Final Boss isn't working (Spoilers)

[Cyrodeus]

As most of you probably know, before you fight Kefka your able to order the 12 party members you took to Kefka's tower 1-12. I heard that the way this works is that when your first party (1-4) fall another party (5-8) picks up the battle.
I was having a surprisingly easy time and beat the first 3 phases in their entirety with my first group (Locke, Sabin, Strago, and Relm if anyone cares) before dying fairly quickly to Kefka proper. Instead of any of my 5-12 characters appearing after my whole party fell I was sent back to my save. I'm just kinda confused and I was hoping someone could explain how the order mechanic works if I misinterpreted it.

[Zunnoab #931]

If you beat a phase with characters down then they are replaced with others on your list when the phase changes. It does not save you if they all die at once.

[Cyrodeus]

Thanks for clearing that up.