I have two stylists in the family, including one veteran, and several hairdresser/beauty industry friends through them. Here's what I've gleaned from listening to them talk:
This varies by salon, but in my experience salon owners typically are tipped, just as you would any other stylist. And in my opinion, it is never rude to offer a tip to a stylist. I've never heard of anyone throwing a tip back in a client's face because they were insulted.
If you would otherwise tip but refrain because they own the salon, please let them know at some point. Otherwise they might interpret the lack of tip as dissatisfaction with their hair. Even if you decide not to offer the stylist a tip, please consider tipping the assistant who shampoos your hair ($2-5 is customary.)
Something else to consider: In many salons, all stylists are booth-renters and thus are all considered to be "owners" of their own business.