It's probably not accurate to say that people join cults, however. The majority of people are actually "recruited" by family and friends who've just experienced something life changing (i.e. read a book or listened to someone speak) and want to share that excitement.
Transitioning periods rather than age seem to be more important when it comes to cult membership. Teens are definitely transitioning, but so are people in their 40s and 50s and the elderly.