A two-timer is someone who is in relationship with two people simultaneously who don't know about each other. If anyone is a two-timer in this situation, it's John. Cassie could be called a third party, but it's not a common usage and it doesn't specifically refer to a secret relationship. Sometimes that situation is referred to as "having someone on the side", when someone is married or in a supposedly committed relationship, but also has a secret girlfriend or boyfriend.

John is doing the two-timing. He has two girlfriends at the same time. He is the two-timer. Judy is just one of his girl friends. She has no label other than a girlfriend. She is NOT the two-timer, John is.