Ask Mr. Smarty Plants

The only member of the Cosmos genus, member of the Asteraceae family, in our Native Plant Database is Cosmos parviflorus (Southwest cosmos). Since the Lady Bird Johnson Wildflower Center is committed to the growth, propagation and protection of plants native not only to North America (excluding Mexico) but to the area in which it is being grown, in your case, DeKalb County, GA, this would not ordinarily be in our realm of expertise. However, we are interested in invasive plants and their control, native or not. By the way, according to this USDA Plant Profile Map on Southwest cosmos, it grows in neither Georgia nor Florida, so it seems unlikely that is the plant in question.

So, we went searching on the Internet for a cosmos that had the potential to be invasive and found Cosmos sulphureus, Yellow Cosmos, which is native to Central America. Since you noted it was considered invasive in Florida, we found this article on Cosmos sulphureus in Floridata. This warning is at the bottom of that page:

"WARNING
Before planting orange cosmos check locally to make sure that it is not invasive in your area. In places like Tennessee orange cosmos is naturalizing in "disturbed" areas but so far is not disrupting native plant communities."

Floridata has the same warning on Cosmos bipinnatus, native to Mexico. In point of fact, Cosmos has been so intensively hybridized that understanding what invasive tendencies you observe in any one cultivar or selection is difficult. Hybrids do not breed true from seed, so the seeds you purchase or the plants you buy may have none of the characteristics you may expect, including invasiveness.  

For one last check, we went to the website of the Southeast Exotic Pest Plant Control article Invasive Plants of the Southeast. Cosmos was not on that list, native or non-.