New York uses your total income to compute a base tax rate. Your actual tax is the NY portion of the base rate. All your joint income will be included in NY income for purposes of computing the base rate, but you tax is the NY percentage of the base rate.
For example, if you and your wife earned $100,000 everywhere then your NY base income would be $100,000. If the NY tax on $100,000 is $x and you earned $50,000 in NY then your part-year/non-resident tax would be 50% ($50k/$100k) of $x.
This is a great answer. I almost feel like it would be better to show both of these in the reporting screen as to avoid any confusion. But maybe that would create more confusion... who knows. Thanks for your excellent reply!