Your situation is a little tricky but you should be able to make it work. When you apply for a mortgage the lender typically requests recent pay stubs (two months) and W-2s (two years) to verify your employment. So your employer is not directly involved in the verification process at this stage and cannot learn any information about the home being mortgaged, including its location or address.
Some lenders may request that your employer provide a written verification of employment but this document has no information about the home being financed, so you are in the clear. In many cases lenders also call your employer prior to your mortgage closing to confirm that still have your job, but again, the lender should not disclose any information about the property location or mortgage.
There are a couple of other points to add that are relevant to your question. First, when you obtain a mortgage to buy a property, you are required to work with a lender licensed in the state in which the property is located. For example, if you want to buy a home in Georgia you are required to work with a lender licensed in Georgia.
Additionally, in general, lenders do not provide applicant information to state governments or agencies without a specific reason. Furthermore, a lender licensed in one state should definitely not provide any borrower information to an agency or government of a different state without cause.
Second, if you are overly concerned you can always apply for the mortgage as a second or vacation home. In this case your interest rate may be higher but you eliminate any confusion over what home (and state) is your primary residence.
Finally, because these matters are so important, we advise you to consult a licensed real estate attorney who can provide confidential legal guidance. A qualified lawyer should understand the applicable state real estate and possibly labor laws and regulations that apply to your situation. Consulting an attorney may cost you a little extra money up-front but can save you significant time, hassle and money in the long run.
"B3-3.1-07, Verbal Verification of Employment." Selling Guide: Fannie Mae Single Family. Fannie Mae, October 2 2018. Web.