When Alera was teaching Tavi, she was saying that part of his attention had to be on furies right in front of him so that his face wouldn't get burned. And the way it was described how Amara flew, I got the impression it was Superman style.
Now, there are the windcoach carriers with harnesses. I think they are more in a Seated position next to the coach, but I really don't know if it's that, or the coach is swinging below them.