My husband worked in NM. We live in AZ. He paid state taxes to NM. How do I assure that AZ isn't also taxing that income? TT doesn't seem to credit the NM tax to AZ.

It sounds like you've set it up correctly. Your resident state (where you live - AZ) lays claim to all your income, from any state, but, your resident state will also give you credit for taxes paid to other states (so you're not double taxed).

When income is earned in another state, that state has the right to tax you on that income only; so your nonresident NM return will only tax your husbands income earned in the state. Any withholdings on the W-2 will work out when you file now. 

You need to update NM first and your resident state last (AZ), for the taxes to calculate correctly, but it sounds like you did so. If not, you just need to delete the state under the state taxes tab and then add it back in, using the correct order.