"...if had I done New York as my first state, TurboTax would have sorted this all correctly."
Yes. In a two-state situation using TurboTax, it's critical to complete the non-resident state return before the home state return. (There are a few exceptions to this rule, all involving the state of California.) This is the only way the software can correctly calculate and apply the "other state credit."
TurboTax has a help article on how to amend a state return:
How do I amend my state tax return? (intuit.com)
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
