Even if you didn't maintain a residence while you were away from Texas, if you maintained your driver's license / identification and car registration there, and if you maintained bank accounts and other ties in Texas, then Texas could still be seen as your permanent state of residence.
If you were only in Arizona and Utah for a few months each for work, you would file nonresident or part-year resident returns for those two states.
Go back to the My Info or Personal section of your Federal return and confirm that you have the correct dates entered for your presence in each state. Be sure also not to count the same date twice when you left one state and arrived in another. TurboTax will need to account for 365 total days for the year or it will perceive an error and not allow e-filing.
As a part-year resident, your wages are taxed by the state in which they are earned, regardless of whether you received your last check after you moved on to another state.
Arizona does tax the wages of remote workers who live in Arizona while working for a company in another state. See this Arizona DOR webpage for more information.
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