@ Larry : it's not automatic but I would say that it's instinctive for some people to react like that since they are talking to a very young people. In a formal situation you have to use "VOUS" even if the person you talk to is younger than you.

Should you automatically use TU if it is a person much younger than you?

I've found that it depends on the teacher, some are more formal in the teacher/student relationship, others are more casual, so I'm not fazed by it. She probably thinks of you as a peer  (or maybe someone younger). You could always that you prefer to use vouvoyer, especially if you want to go through the "natural progression" of establishing relationships in French culture.

Thank you for explaining. A teacher once told me it was rude in the french culture to say "Tu" to someone you don't know. But maybe these things are different from a situation to the other.

She tell you "tu" because it's a friendly person. If you would't (dis lui:"vouvoyez-moi madame")