What decides the turn order in Bravely Default

You can easily check the base stats of each character under the "status" menu, in "tactics."

I'm currently playing through at level 13, so my stats may differ from yours; however, the base values for my current party are as follows:

Tiz: Str 16 Vit 16 Int 15 Mnd 16 Dex 16 Agi 14

Agnes: Str 14 Vit 14 Int 17 Mnd 17 Dex 14 Agi 13

Ringabel: Str 15 vit 15 Int 16 Mnd 14 Dex 17 Agi 17

Edea: Str 17 Vit 17 Int 14 Mnd 15 Dex 15 Agi 14

So as you can see, Edea is suited to be a fighter-type; Ringabel, to be a faster type, a la thief or ninja; Agnes is best as a mage; and Tiz is an all-rounder with slight leanings toward Mind-type or Strength-type jobs.

Edit to add: However, the other poster IS indeed correct that the difference is pretty small, and mostly insignificant. As a minmaxer, though, the difference between 17 base Dex and 14 base Dex is pretty huge early in the game.

Having tried to build a tank in that game, I can tell you it doesn't work. At least, not the way it would in a MMO "holy trinity" type of game that most people think of when creating party structure nowadays. The items that make the equipper more likely to be targeted only do so by a small amount, certainly not enough to be noticable in my experience.

To answer your question, the enemies will decide who to attack on their turn. That is: when they're about to go, right before each hit, assuming they don't brave. They are also reactive to what your characters have done, not to what they are about to do. If you queue up a 4-brave healing spree, the aggro is generated when those heals are cast, not before.

Granted, even with the aggro, there seems to be a random factor involved to prevent "perfect" tanking. Because of this, the game seems to encourage powerful healers and group durability more than glass cannons and solid tanks.