Usually turn order is determined by the character initiative. When two characters have the same initiative, the system will attempt to "balance things out" by interspersing characters from different teams.
For example, the following match consists of two teams, both team using a party of Ranger (RA), Wizard (W), Rogue (RO) and Warrior (WA):http://imgur.com/a/DJQxL
Notice that the turn order is Red WA, Blue WA, then Blue RA, Red RA, then Red W, Blue W, and finally Red RO, Blue RO.
This turn order is "slightly" in red team's favor because
1. He gets the very first move before anyone else.
2. There's a bit of a pattern break at the end: Blue Rogue should've moved before Red Rogue.
However I would say it's decently fair. Not perfect, but decent.
Things don't work so well when both teams have exactly the same initiative for all of their characters:http://imgur.com/a/64gBM
Notice that turn order: Blue RO, Red RO X 4, Blue RO X 3.
This is HIGHLY problematic. Blue team is now in a serious disadvantage: with the entire red team moving right after blue moving only once, he is most likely going to either lose map control or lose characters right off the bat in the first turn! And there is nothing he can do about it. In case you are wondering, this behavior is consistently reproducible with any similar setups where all characters have the same initiative from both teams. Things are relatively benign when it's all rogues. When it's all wizards or rangers, half way through the first turn Blue would have half of his team left and no way to do a thing about it, because he hasn't moved yet! Not cool.
Ideally, the turn order should have red and blue moving one after another with the first person to move switching hands as it goes (within the confine of the order determined by initiative of course). This is clearly one of the cases when the system doesn't work as intended.