No.....he does not.
HE remains a TX resident, no matter where he is posted or trained...throughout his Military service since TX is his Home of Record.....and also his State of legal residence. His military wages will always be considered TX income only.
He would only have to file a non-resident state tax return for some state he is posted in...only if he works a civilian job there while off-duty (Or, at some future date, ends up owning a property in some other state, that he rents out to others for extra income)
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While it is possible to change a military person's State of Legal Residence (SLR) while in service....a TX resident would rarely bother to do that.....Read: