It is not so much that hot tubs don't use that chemical as it is a by product of the chlorine most used in a spa. CYA, aka stabilizer, is a weak acid needed in outdoor chlorine pools to protect chlorine from the sun which will deplete it. Spas, being covered most of the time, do not need CYA, nor do indoor pools. The chlorine most suitable for spas is dichlor. It is fast dissolving and pH neutral, but it is also almost half CYA by weight. It is one of two stabilized chlorines, the other being trichlor. Outdoor pools want at least 20 ppm CYA. There is no added stabilization benefit over 50 ppm. When very high stabilization occurs, chlorine becomes less effective as a sanitizer and must be compensated for by using more chlorine.
Think of CYA as little umbrellas that protect chlorine from getting sunburnt. With the proper amount of protection, the chlorine can go about doing its job effectively in the shade. If you have too many umbrellas, they start to get in the way and the chlorine has to maneuver around them to work thus slowing down its efficiency.
The only way to reduce CYA is to drain or partially drain and fill. Now some of this occurs with normal use as water is spashed out or removed while exiting a spa. Pools with filters that are backwashed loose water and CYA that way. So every time you add water, you reduce CYA.
Most of this is a moot point with spas. The small body of water almost guarantees your CYA levels will rise quickly, but the reduction in chlorine effectiveness doesn't have the downside it does in a pool. As long as you change your water on a regular basis (I change mine every four months), don't worry about CYA.
I don't know how accurate test strips are for CYA. If you are really interested in CYA levels, get a drop kit.