Yes. Even though you are in New Mexico temporarily for training you are earning money so your wages are taxed by NM.
New Mexico says:
"New Mexico imposes a tax on the net income of every resident and on the net income of every nonresident employed or engaged in business in, into or from this state or deriving any income from any property or employment within this state."
Arizona will give you a tax credit for tax paid to New Mexico on your double taxed income. You will have to file two tax returns next year - an Arizona resident tax return and a New Mexico nonresident tax return.
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