It varies from person to person, but in general, it is better to keep in touch, because a word from the tutor can determine the fate of a student, especially if he is admitted to another school.
Of course, you don't have to contact, provided that you are particularly excellent, and you are in the top of the exam, and your score is there. Don't be unreasonable. The sooner you contact, the better. Just cultivate more feelings. Generally speaking, when a teacher says he is looking for you, it means that you have stepped into the gate of this school.