A canter is 3 beats, and you will move your seat in three ways. You have UP, DOWN, SLIDE. Sometimes it’s easier to think of it as UP, and then DOWN-SLIDE as a unit.
If you jump horses, you know SLIDE, because that’s how you adjust your horse’s stride before a fence.
If you ride dressage, you know UP, because that is how you collect and create more volume in the canter.
If you ask for a transition down from canter to trot, you do that with your half halts coordinated during DOWN. But if you want Canter-walk like in your simple changes - ask during the UP.
(Pro-tip: If you do that on the DOWN phase of your posting trot with your outside rein you will have a perfect square halt too!)
Do you ever get jealous of those people riding around with a perfect and quiet collected canter that looks effortless? I sure do. I spent one summer showing a pony that the judges would put “off to the races” in the comment box and I just thought it was because she was spicy. It was actually my seat! I was pushing her too hard during the SLIDE phase of the canter and it was driving her too much. Instead, I had to learn how to ride the up, which is more of a lifting phase of the canter. As soon as I learned how to ride the UP, my horses could magically slow down and collect their canters. Funny how that works! (But obviously if you have a torpedo butt and never sit in the saddle you have to sit in the saddle and start riding the down-slide before the UP..just sayin).
The bottom line...if you want to look better in your dressage test and have more influence over your horse, start riding the UP phase of your canter.