Ask to view their portfolios of previous work. I'm sure they don't do it in the same place as cutting hair. It's a different room yeah? If it's not I'd probably go somewhere else. I've never seen a hairdresser and tattoo parlor together before hah sounds cool. I used to be an apprentice tattooist so I think you should ask them and if you know anyone else who's had tattoos from them? Good luuuck :)
Actually funny you mention that because I JUST the other day saw a place that had exactly the same combo, it stuck out as unique but I wouldn't not get one just because of that, I'm sure they two are not done closely together and it'd be interesting to watch people get their hair cut as you're getting tattooed. Also, if the artist is good why wouldn't you?
There this place in my city that does piercings, tattoos, and cuts hair but each is a separate set of rooms and is so clean and professional. So as long as the rooms are separate, I do not think that it would be a very high possibility.