At least, he didn't teach what most people think of when you say "Constitutional Law." He taught things like "Current Issues of Racism and the Law" and "Voter Rights." Sure, those courses touch on Constitutional Law, but as far as I can tell, he never taught the basic Con Law courses. I think calling him a "Con Law professor" is meant to make his work at UC more grandiose than what it was. I'm not denigrating his work there; I'm just calling it what it is.
He did get promoted from adjunct to "senior lecturer," but he was always part time. (I'm not sure what the difference is, since they are both part time positions. Perhaps one pays more, or guarantees more classes? Who knows.)
He was barely a senator before he started running for President. He was a state senator, though.
I give more credit to running and owning a company, than I do his other experience.
To each their own.