Can you name the antibiotics he is taking?
I suppose you are talking about macrolide (like azithromycin or clarithromycin), ethambutol, and rifampin.
Joint and muscle pain can be a side effect of some of these antibiotics, particularly ethambutol. It's also possible the pain is related to the MAC infection itself.
In many cases, if the pain is a side effect of the medication, it will go away once the treatment is finished.
Since his sputum tests are clear, it's a great sign that the treatment is working. Still, you should discuss the pain with his doctor, since he is introduced to all the meds he is taking and can prescribe some analgesics to manage it.