I have somewhat limited experience of tutoring but I would say that you should let your students decide what material to use. Often the parents will be concerned about exams so it can very much be a case of sticking to the Curriculum, but if you build up a long-term relationship with any particular student you might find that you get the opportunity to be more flexible as to what you teach, and how. But in the end the role of a tutor is to help the student when they are having difficulty, so you should let them decide what they find hard and try to help them.
My limited experience means that I'm yet to have any horror stories. Hopefully it will stay that way! One word of advice, though -- there are often more tutors than there are people looking for tutors, so you may find that you take a while to get a student.