A musty smell can have many causes. For example, residual dirt can be flushed out of the pipe system after a basic cleaning. This is a longer process that can take up to 2 or 3 months. Poorly cleaned filters can also be responsible for odour formation.
Whirlpool water or whirlpool cover?
Often it is not the whirlpool tub water itself that smells, but the edge of the whirlpool tub where the insulating cover rests or the edge of the insulating cover itself. There may also be foul water behind the cushions. As all these "sources of odour" are directly at face level when bathing, the impression is often given that the water in the whirlpool tub itself smells unpleasant.
You can check this very easily. Take a glass of water from the whirlpool. Walk a few steps away from the whirlpool and smell the glass. If the water does not smell now, it is due to the rim or the insulating cover.