In the ongoing conversation about domicile and residence, one important issue can not be emphasized enough: taking a homestead exemption on your real property taxes for a house is a huge indicator of where you consider "home." In fact, in many states, the homestead exemption application has a statement something like this, "I declare that I am a legal resident of the state of {blank} and this is the address from which I will file my state income tax return," or similar language about your residency in that state.
A homestead exemption is any form of reduction of real property taxes (real estate taxes) that is based upon your residing in a property that you own. In most cases, the homestead exemption is designed to be taken/given to legal residents of that state.
This can be a tricky issue, and also an expensive issue. It's tricky because some states automatically grant the homestead exemption to property owners who use the property address as their mailing address, or file their tax returns from that address. More and more states are moving away from automatically granting the homestead exemption and are now requiring that you physically fill out an application to receive the homestead exemption.
Then comes the expensive part: the full tax burden on a house or other real estate can be significantly higher than the reduced rate permitted by the homestead exemption rules. I have seen real estate taxes that doubled when the homestead exemption was removed, though it isn't usually that drastic a jump.
Homestead exemption rules are state specific, and I don't have a handy-dandy chart of every state and their details. Some states could offer a homestead tax break to military non-residents, and some states will allow resident military folks to maintain their homestead exemption even if they receive PCS orders outside of the state.
In the past, the ability to track residence and homestead exemptions was limited and many jurisdictions didn't bother double-checking eligibility. As state and local budget continue to shrink, the governments have a larger interest in making sure that everyone is paying their full tax burden. In addition, technology has made it easier to cross-reference those who are claiming homestead exemptions with those who are filing state income taxes or engaging in other "resident" actions. If you are found to be taking a homestead exemption for which you are not eligible, there are two possible negative outcomes: some sort of penalty for not paying the higher, non-exemption property tax, or the state in which the property is located claiming that you are actually a resident and charging you state income taxes for that state. If you're not a resident of the state in which your property is located and you are physically residing, there is probably a good reason why you have chosen not to be come a resident. It would be a huge bummer to have that messed up!
Unfortunately, you can't always rely upon your local tax officials to understand all the nuances of the rules as they apply to military families. Please be sure that in addition to speaking with your tax officials, you do a good chunk of your own research to ensure that you are paying the lowest possible taxes while staying within the law. You really don't want to get this one wrong.