As a New York resident, all your income is taxable by New York, regardless of where you earn it.
Unlike New York, California does not have a "convenience of the employer rule." California taxes non-resident employees only on income earned from work physically performed within CA. Your employer should withhold CA taxes only on that portion of your income. See page 19 of this CA tax publication:
https://edd.ca.gov/siteassets/files/pdf_pub_ctr/de44.pdf
CA does not require that a non-resident have a CA address in order to have CA taxes withheld. In fact, California Form DE 9C, the form on which the employer reports withheld taxes to the state, does not even require an employee address.
https://www.dir.ca.gov/dlse/regulation_detail/de9c.pdf
The address on your year-end W-2 should be the address to which you want it to be mailed. There is no rule that says that that address cannot be a PO Box. Your state tax obligations are not determined by the mailing address on your W-2.
Your situation is common and can be handled by the TT program.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
