You seem quite tense, especially throughout your arms and your back which is causing your horse to turn upside down. Another part of this is that you are leaning a little bit to far forward. Since your legs are in a good position, bring up one of the photos of you riding, grab a ruler or a straight edge, and hold it to the screen so your heel and your hips line up. See how much your shoulders point forward?
I would also like to see your hands moving with the horse a little bit, since your arms are stiff your horse is turning inside out (in most of the photos) probably due to a mixture of your tense arms and possibly hasn't been trained to collect himself. If you watch horses move with a very loose rein or out in the pasture, you will see their head bob and move forward with every movement as well as a little bit of moving up and down. If you ride without moving your hands with your horse, he can not balance himself by using his head and neck, which leads to not so fluid gaits, and him either trying to balance by pulling on the reins or lifting his head.
When your horse is walking, let your reins out loose and put your hands on his neck and feel it moving. Now, what you want to do is to try to mimic that movement with your hands as you are walking without putting them on his neck and try to do this at other gaits. Moving your hands with your horse is especially important at the walk and canter.
Like I said, you have a great leg and you look up. Just be sure not to lock up your arms or lean to far forward
ETA: I based this all on the show pictures, just to let you know.