There's something about moxa that causes really nasty looking burns - ouch! But, I have never seen one become infected, maybe due to the tremendous healing nature of the stuff. You do say it is getting better so, no harm done.
As for 'missing the point' I often give sticks to patients, usually for turning breech babies but also for St 36. St 36 is a big point, so I tend to think it's OK if they are not spot-on. And never forget the power of intention! You are right, though, this stuff needs careful handling.
Hope he gets well soon. If it's troublesome, lavender oil is good. It can be used neat on the skin (unlike most other oils) and when I was a nurse in a burns unit, we used it all the time on small lesions with great success.