During the Kybella (or other deoxycholate) treatments to the neck/under the chin fat, there is typically only a 6mm long (1/4 inch long) needle used for the injections.....which should not put the salivary glands in harm's way. Nevertheless, it is generally better to take care of medical conditions (such as salivary stones) PRIOR to having a cosmetic procedure done that is in the same general area. In the case of the Kybella, the resultant huge amount of (expected) swelling might cause the area of the stone to get irritated. So, to use an old phrase, it is better to be safe than sorry.