If you are paying tax to MA, we assume you must have MA source income. As to why you are seeing some amounts that are auto-populated, it could be that if you used TurboTax when you were a MA resident, then some of those income amounts may be showing up on your AZ return.
Regarding completing your return, it appears you are completing your state returns in the right order. That is, complete your non-resident state first (MA) in order to determine your MA tax. Then prepare your resident state return (AZ). You are correct in that the AZ part of TurboTax will ask about taxes paid to another state, and the reason for such a question is to ensure that you get the proper credit on your AZ return for having paid tax to MA on income that AZ would also tax.
Make adjustments if you feel adjustments need to be made. Also, follow-up with additional questions as needed.
@almargahi
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