It's one of the myths in the hobby. A cleaner shrimp or cleaner fish doesn't rid a fish of parasites that are below the fish's surface, or imbedded in the gills. I wish it was otherwise.but I read cleaner shrimp are pretty good at pest control.
Sounds good. Keep up water quality and feed the fish all it wants to eat. Don't overstock your aquarium.The tang seems to be stress free