To "work out of somewhere" means that you are based somewhere. At one time it was usually used of someone whose work involved travelling. A salesman might "work out of New York", meaning they were based in New York, even though their actual time was mostly spent on the road (and therefore not in New York at all). His office-bound colleague would be said to "work in New York". In more recent times 'work out of' used as a synonym of "work in".
The phrase you ask about therefore strictly means that the job is based in Atlanta, that they will report to someone in Atlanta, and they will be paid in Atlanta. However in reality it probably means you need to be present in Atlanta. The phraseology might open the door a crack to the possibility of telecommuting or remote working.