MPS is an oxidizer but not a sanitizer. Chlorine is both an oxidizer and a sanitizer. Oxidizing is breaking down waste like sweat and skin oils. Sanitizing is making sure bacteria and the like can't grow. So basically MPS can be used to break down bather waste but you need some chlorine or bromine too as a sanitizer since MPS cannot do that job.
The advantage to MPS after a soak compared to adding bleach is that it can break down the waste without producing CC's. So if you are having an issue with CC buildup from using only chlorine, the use of MPS immediately after using the tub to break down bather waste can be an advantage here. However after the MPS has had a chance to break down waste you must add and maintain an adequate level of FC to ensure a sanitary hot tub.