No, unfortunately, you may have misunderstood. If your wife is working in a non-military capacity, she will pay taxes to the state she is working in (AL). Her income would also be reported in Texas if they had an income tax.
Please see item 7. Common misunderstandings and uncertainties.
Military Spouses Residency Relief Act (MSRRA) (Public Law 111‐97)
c. The MSRRA does not relieve the spouse from paying State income taxes on income other than for services performed in the non‐domiciliary State. For example, income from the sale of real property or from the rental property would be taxable in the State where the property was located, MSRRA notwithstanding. The spouse must also comply with the tax laws of the domiciliary State
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