Firstly - you will need to get the phrase right! It is rUb off on me. It comes from how you rub something against something else, some of it sticks - like if you rub a painted item on some wood, some of the paint ends up on the wood. You generally use it with personal characteristics, such as madness, happiness, enthusiasm, as your student suggested.

Usually the term, rubbing off on me, is used as a way to express people are become alike one another. The way good friends start saying the same sayings, start doing the same things. My mom had always been a good driver, but over the years my dad's bad driving habits have rubbed off on her.