As the spouse of an active duty servicemember, you are permitted to use his State of Legal Residence (SLR) as your own home state for state tax filing purposes. You may also use your own home state if you prefer. It's your choice.
So if your servicemember's spouse's SLR is GA, you may choose to file only in GA.
You should have filed for state tax exemption so that your employer does not withhold taxes for HI - but they will withhold taxes for your SLR. This is under the Military Spouses Residency Relief Act (MSRRA).