For the military member, their HOR (Home of Record) is as shown on their LES, and does not change unless they take physical action at the personnel office to change it.
For the non-active duty military spouse, the SLR (State of Legal Residence) is the same as it was before you married or before one of you joined the military (whichever occurred last), unless the spouse took action to change it.
Now for the non-military spouse, if you have income earned in another state outside of your SLR, then depending on the SLR and the state that income was earned it, you may not have to pay that state any taxes on it. This is covered in the MSRRA (Military Spouse Residency Relief Act) of whatever state you earned the income in, if that state has such an act. (almost all do.)