OK - you should claim the "other state credit" on your NY tax return, not on your CA tax return. Your compensation for the vested RSU's would be taxable by both states, so it's only the tax you paid to CA on that income that you can claim on the NY return. All the income you earned after becoming an NY resident is taxable by NY.
When you file two part-year resident state returns as you must do, TT recommends that you complete the former state's return before you do your current state's return.
How do I file a part-year state return? (intuit.com)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
