That's correct. Puerh tea particularly has very strong "ChaQi" which is (part of) why people prize it so much. Some other teas have it as well, and it's really not just caffeine but something much more interesting and deeper. Real ancient tree puerh (for example [1]) or very old tea are excellent examples of teas with a lot of ChaQi

[1] [link redacted] Edit: both the site and the rambling about this tea and its ChaQi are mine (it's the best example I could think of from the top of my head)