I have never heard of an advanced rider rising incorrectly to the speed of the horse. Even Mannie above said she likes your tempo. You would not get a good tempo if you were rising incorrectly.
If you are out with your rising you will land on the back of the saddle or on the cantle. Beginners start off rising too high.
You are landing softly in the middle of the saddle and I do not see anything wrong with it.
Yes you can speed a horse up by rising faster, you can slow your rising to slow a horse. Advanced riders do not need to do this, they ask for the trot with tempo and go straight into the trot they want from the first step…
You do need to be sitting up a bit straighter to influence with your rising. At the moment when you lean forward you are actually pushing backwards when you don’t mean to. Leaning back you push the horse forward without meaning to. Just like Goldilocks you want to be in the middle so you can push either way when you choose to.
I will say again look up and sit on your butt.
If you are fighting a jump saddle, a well fitting for you and your mare, dressage saddle will help.