That’s not how it works. What matters is the state of your residency and the state that your paychecks come from. If you get paid in a state you don’t reside in, you have to file in both, unless there’s a reciprosity agreement. Many states will allow deductions for income tax paid in another state. So for example if the state your employer is in has a 4% rate, and the state you reside in has a 6% rate, then you’d end up paying 4% to state A and 2% to state B. It is possible to get double taxed depending on which states are involved.
So the CEO will at the very least have to file in California.