Earlier quoted context omitted.
No, state personal income taxes are based on personal income you earn in the state . If you work in multiple states, you file in multiple states.
That depends on reciprocal tax agreements. [1] He will have to file in both states, but what he pays will depend on several factors. He will likely get tax credits in California, but I am not a tax attorney or a CPA. Elon could probably give some indication on how much he is saving if he is saving anything at all. [1] - https://www.optimataxrelief.com/live-work-pay-taxes/
It's simply not accurate to make the general statement that state personal income taxes are based on your domicile.