If you are in doubt then ask if you can talk to somebody they have tutored - to get first hand reference.
I'd also say:
Make sure you get first hand experience and then direct experience. It's your DD or DS and you know him/her better, nobody else can decide whether they are assisting in what is needed.
And above all, trust your instinct. If you feel anything is not right, it probably is. I'd say walk away. The reality is many tutors are selective about the children and families that they take but so should you.
And similarly to when buy anything, you may even like the salesman's pitch but it's the service that makes the difference..