There are caveats as mentioned in this thread, but in general, no you do not pay CA taxes if you live in another state and your company's HQ is in CA.

It depends on what state you're a resident of and where you do your work.

I live in MA and, when I worked in NH, I had to pay MA income taxes because I live here even though NH has no state income tax. Now I work for a company with offices in MA (even though that's not where the official HQ is) so I still pay MA taxes; doesn't matter if I'm remote or not. Were I to move to NH and work remotely, my understanding is I would then not pay state income tax (although I would if I were assigned to an MA office).