In battle, your three youkai in front actively fight and for the most part control their own actions apart from their special attacks (though you can teach how they act in battle by letting them read various books). You can spin the wheel (in real time) on the bottom to move your team to switch them out. Placement of your youkai is important since you can't just drag and drop them where ever on the wheel in battle, only rotate.
It probably sounds more complicated than it is whern you're actually doing it. Are there any off screen videos that show battles maybe?
Also, since this is a general thread. How's the anime? I'm not much of an anime watcher (not at all really) but for this game I wouldn't mind getting into some of it's lore before I get the game. Which will hopefully be some time in 2015 for Europe...