It depends.  New York has complicated laws when it comes to telecommuting.  In general, they consider that the income you earn for a NY company while working from your home is more of a convenience to you than to your employer, and, because of this, will usually consider that income as taxable in New York.  You will want to check with your employer to ensure that the income you earned while you telecommuted from your new California residence is not taxable in New York.  What determines whether or not the income earned in California is or is not "NY State Source income" depends on whether or not NY is allowed to tax the income or not (not whether or not tax was withheld or not).  

As far as the returns themselves are concerned, you are filing part-year returns to each state.  The only question is whether or not some of the income is also New York nonresident income.  This would be the telecommuting income if New York is allowed to tax that income.  If they are, then your part-year return will include all of the income from that employer, with the portion earned in California (box 16) being reported on the return as income earned while a nonresident.  You will want to prepare the New York return first either way.  Here's an FAQ to assist you with this:  https://ttlc.intuit.com/replies/3302052

California taxes that portion of income no matter what, because you were living in California when you earned it.  If New York also taxes that income, California will give you a credit for the tax you pay on the telecommuting income.