I had a replay to explain QuickFix jumping, but it crashed TF2, so I'll just explain it manually.
Basically QuickFix jumping has three factors considered when that Soldier or Demoman performs his jump.
1. Are you touching the ground? If you're in the air for any reason when they jump, say because you were bunny hopping or dropping down from a ledge, then you won't go anywhere. This also means that stuff like pogoing, multi-det air jumps, and wall jumps are all out.
2. Are you moving? If you're not moving then you'll be given the horizontal and vertical vector that the Soldier or Demoman achieved from their jump. You definitely don't want this though, as usually the teammate will jump from the edge of a platform, while you'll be pulled along from the middle of the platform. They'll then just barely land where they want to, while you'll fall two stories to massive fall damage.
3. If you are moving, you overwrite the horizontal vector's direction. This means that if you're moving backwards when the teammate is jumping forwards, the two of you will go in opposite directions. I'm unsure if the magnitude stays the same, and I kinda hope it doesn't, as your faster running speed would then allow you to keep up with the Soldier or Demoman even if they started their jump ten feet away from you.
I think, but this also has to be looked into, that if you jump at the exact moment the teammate blast jumps, the force of your regular jump is applied to the magnitude of the vector in some way. Horizontal only or vertical and horizontal, I'm not sure.
Finally, regular air control (strafing, etc.) rules apply.