The picture above was a handout from my first day in class. I can see where I cleaned up some of the spots, as it was copied off a copy made off a copy, etc. This family tree was as of 1988. It says Yang Shau-Chung "still in Hong Kong" and Wang Tyzz-Her (Zhihe) "still in Taiwan." I don't know if that's true as of 2014. My teacher, Ho Chin-Han, was a student of Deng Shi-Hai, who was a student of Wang Zhihe. In Chinese, the family name is first.
For the majority who practice tai chi, especially in the US, lineage is not important. There are no kung fu belt colors in the original art. The same can be said about karate. Most do tai chi for the exercise and the health benefits of the exercise. Tai chi, like walking, is an excellent, inexpensive form of exercise. It isn't necessary to buy stuff like kung fu uniform, kung fu shoes, weapons, or even audio devices. You get plenty of benefit, plenty of workout, just doing the warm up, chi kung, and long form. In my opinion, anyone who's giving out tai chi certification is doing it to promote their business or school, much like rah-rah karate belt factories create extra intermediate belt $tripe$ to keep the kid$ motivated to keep coming to class & test$ and renewing their contract for another year or three.
I can't say it was tradition, I don't know. It used to be a teacher would have a following of students. The relationship would extend decades. I don't know how teacher or student made a living. Teacher would have senior student lead the workout, then maybe eventually take over the class while he supervises once in a while. Teacher might have several locations and do the same with other senior students. But students come and go. Maybe senior student who ran the class for many years gets a job transfer to the US and gains his own following. Finally, teacher decides he's not going to teach anymore and leaves his classes to a senior student who is still with him. No rank, no certification, just hierarchy and loyalty over the years. You would think that the longer you're with a teacher, you would get more instruction, details, and insight.