No. The Veterans' Benefits and Transition Act follows up the Military Spouse Residency Relief Act (MSRRA). The MSRRA says the spouse must be in the state solely to be with the military member. Since your spouse is also stationed there for military duty, the act doesn't apply. Here is a link with more detailed information on the subject.
Your spouse can however change their state of residence with their finance office and by taking steps to make a state their new resident state. Things like registering to vote, registering vehicles, getting a driver's license, as well as being married to someone who is a resident there, would support the state as their resident state going forward.
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