Yes, you're filing joint return; so, it's going by the state field on the W2 without regard for which person that W2 was for.
As to the "credit for income tax paid into another state"; you'll get a box with the amount of income double taxed pre-populated. You have to look at that number closely. It may be (frequently is) necessary to figure out the right number to enter there (change the pre-populated amount).
Your best bet may be to use "override" and make your entries directly on form IT NRC
