For the most part yes.
Most states will tax you on the income you earn while physically present inside their state. Each state has a different filing threshold, however, if you meet that threshold, you will need to file a return in that state.
Then, you will need to report ALL the income on your AZ return. You can then take a credit for taxes paid to the other states on the same income on your AZ return. So be sure you fill out the non-resident states prior to your resident state.
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