This dawned on me more when FF4A came out.. but basically.. there is a battle order priority of your characters, based on their position, unlike FF5/6.
This applies mainly against "First Strike!" attacks, but also if all character agility were equal (it isn't usually the case in most instances).
This totally ignores what row your character in.
Here's the order:
1) Middle
2) Top Most
3) Bottom Most
4) Top-Middle position
5) Middle-Bottom position
The most obvious way of seeing this grouping is via saving.
The benefit of knowing this is trying to align your characters in such a way to determine who goes first. I would assume most people would try to align characters with high AGI along the top 3 positions... and eventually leaving Rosa in the 5th position at the end of the game. This also helps in attempting the Silver Shield on Rydia trick/bug.
Edit:
Additional Note: This order behavior also applies character addition/joining and level up messages.
We have EVEN MORE themes now, but some old ones are gone...