It depends.
I have gone to an airbrush tanner for a few occasions, and I have gone both ways. When I had airbrush tanning done for my wedding, I did not tip. The woman I saw owned her own business and she had a service charge for a single person built into her fee (she waived the service fee if there were 3+ clients for a wedding) so I did not feel I needed to tip beyond that. When I had a tan done at a salon, I did tip the airbrusher.