I think that one of the most important questions for parents or students to ask a potential tutor is what their teaching style is like. Is the tutor strict, gentle, authoritative, a "study buddy"? Assuming that a tutor is qualified in their subject(s), the most necessary thing is that they get along well with their student's learning style and that they "click" as a pair. Having a tutor that understands the student and responds to their needs outside of their work can be essential for a pleasant and even fun tutoring experience.
As a tutor I definitely tend towards the encouraging and "study buddy" style of teaching! I don't usually assign tasks to complete alone or preside over a silent homework session, I chat with the students and help talk them through their work or any questions they might have. This seems especially helpful for younger students; a bit of positive reinforcement can go miles with a shy or beginning student, who may not have yet adjusted fully to the discipline of school and homework.