I'm not sure if that actually affects in battle action order. What it certainly affects is the begin of battle action order. It's more important for players who uses multiple clone/puppets as different placement order could result in different clone placements.
Note that moving any character will place that character into the 4th slot for this purpose, so you dont have to remove your ninja from team to readjust this, just move stuff back and forth.

The mystery order is ALWAYS the same as normal attack order
You don't "cast" normal attacks.
so no, that's not it.

I don't recall(note it doesn't mean it doesn't happen, just I don't recall) ever seeing a fight where mystery cast at the beginning of round go off in a different order than the standard attacks. Granted I don't pay close attention to every fight and I personally only cast everything at the beginning if enemy isn't faster or enemy have no interrupt(including chase chain ones), so only about a quarter or so the fight was observed for this, and usually only the first mover (it's tedious to try and observe every mystery user every fight, first caster being more important, I mostly focus on that)
So until I see evidence to the contrary, I will stand by the belief that it's the same order.

Granted, the order might be RNG or depend on who click faster if there is a tie in init, I'm not sure if init is equalized in arena and I don't play arena enough to really tell. And outside of arena, ties are rare.