The dragon punch input in SF4 is notoriously easy to trigger--down-forward down-forward is all that's needed to trigger it, because the game counts the first df for both the forward and the down input of the DP motion, forward, down, down-forward. Since you are often jiggling through the down inputs while crouching, it's easy for the game to interpret a dragon punch. You're not alone, many people have this problem and give the SF4 games flak because of it. I think the square stick gate on TE sticks exacerbates the problem slightly, because it can be difficult to get a straight horizontal input, as opposed to a diagonal one.
When going for things like cr.MK xx fireball, a dragon punch can happen when you hit the button while the stick is still on down-forward, instead of forward. Be sure to follow through with your fireball motion, making sure you hit forward, and then delay the button press just slightly so that you are definitely hitting it after the motion.
In fact, it can help to go all the way from down to up-forward, making a 135 degree arc instead of 90. This explicitly makes sure you hit the forward input. This is useful in a lot of cases when the game has trouble distinguishing inputs. For example, it's especially helpful when doing M. Bison's Ultra 1, which has a very bad habit of coming out as a teleport. Instead of charge back, forward, back, forward + kicks, you can do charge back, forward, back, up-forward + kicks, which makes sure that the game sees the forward input instead of down forward.