Your earnings during the time you were a CA resident are taxable by CA. Your earnings after becoming a resident of NY are taxable only by NY, even though you were still working for the CA-based company. (CA does not tax non-resident remote workers.) You became a NY resident (and ceased being a CA resident) on the day you began living in your new home in NY.
You'll be filing a part-year resident return in each of the two states. This FAQ explains how to do that in TurboTax: https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
