If you are a W-2 employee (as opposed to an independent contractor), then you are correct that your income earned for remote work done from TN is not subjection to CA taxation.
If you move to CA in 2020, then for 2020 you would file your CA tax return as a part-year resident, not as a non-resident. Income you earn after you become a CA resident is entirely taxable by CA. On that part-year resident return you would report ALL your CA withholdings for 2020, which would include the amount withheld before your move. CA would then refund any excess withholding. Your CA-source income on that return would consist of the amount you earned after becoming a CA resident.
You become a CA resident for tax purposes once you're "in CA for other than a temporary or transient purpose."
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
