In addition to Baze gaining tm when you get buffs, he is also a Rebel. If opponent has Luke leader zeta, then he gains tm when opponent debuffs are Resisted. Also, if Binds All Things is zeta, then he will also gain tm when their CLS lands debuffs. A CLS who also gets tm if Baze is damaged while he doesn't have Call to Action.
As someone said, tm gain and speed are two different things. Imagine if they were all runners--speed is how fast they go, and tm is the length of the track. A tm push is not them running faster, it's them teleporting farther down the track.