Its based on turn number (the action number in your ninja team) and initiative.

Say the fields are set up as so:

Your Team

** Move3 Move 1

** Move4 Move 2

** ** **

Opponent(visualize this as being across from you)

** ** **

Move1 Move2 Move3

** ** Move 4

Now if you activated your mystery from your Move1 and they used Move1 the only thing that would take precedence is Initiative. SO if your opponent is faster he'll go first. Columns and rows don't mater...that only plays into a particular strategy. Now say you activated your mystery from your Move 1 and they for some reason had Sasuke In Move2 they only things that would stop you from going are: 1). Your myst is a non prompt meaning you'll have to wait until people cycle through their standards. 2) Terrible luck, or a timeout which lagged you out and caused a delay in using your myst. Aside from that, generally speaking initiative always wins if mysteries are triggered from the same Move slot.