Reining saddles come in different kinds because not everyone likes to ride the same way.
Many tend to be best a bit larger than you need and slick, so you can move in them as you need, for little adjustments.
In reining, you are not stuck in there in one spot only and that is harder to get used to for those that want to be stuck inside a saddle.
The trainer I started learning reining explained that and that he has English riders take right off correctly because they are not so set in trying to stay in one single spot, like many western riders try to do.
Now, for working cowhorse, you may use a little deeper seat, that will help you stay in the saddle better in the wild turns on cattle on the fence.
My ranch saddle is a 14 1/2" seat, the reining one is 16" and both feel right for the intended purpose.
I agree that the saddle in the pictures seem to need at least a larger pad, that one looks almost too small.
If that saddle doesn’t feel right to you, try another type, there are all kinds of reining saddles out there.
A good reining trainer can look at you and have an idea of what kind of saddle should fit your built, your leg and bottom best.