Just as athletes use a variety of workout equipment for their training, it is logical for brass players to work out away from their instruments.
I found the CTS-provided exercise logical and very useful. It exercises the muscles responsible for brass playing and aperture formation with numeric feedback, which, for someone who loves numbers and readout, is a reassuring experience.
After one week, I already see progress in my upper register and endurance. I will keep using it until I see my reading go from 110 torr to 160 torr, which is about 3 psi, according to Arnold Jacob, which is all any brass player needs to play anything physically.