According to the following website the employer is not obligated to refund you the California taxes erroneously withheld. You will have to file a California state income tax return to get a refund of the state taxes withheld.
Contact the California FTB for assistance - https://edd.ca.gov/en/payroll_taxes/FAQ_-_Military_Spouses_Residency_Relief_Act/#:~:text=This%20Act%....
