The artist wearing gloves isn't all that constitutes a clean tattoo experience. Your artist should exercise Universal Precautions by OSHA. This means barrier protection over every object or surface that could come in contact with either their hands or the tattoo. Everything should be disposable.
They should have bags over their wash bottles, machines, clip cords, and plastic over the work surface in the immediate tattooing area. Needles and ink should be disposable as well. Tubes should be sterilized in a medical-grade autoclave.