Vaccinium ashei (rabbiteye blueberry) is native to the American southeast, although it does not yet appear in our Native Plant Database, which is always a work in progress. From Texas A&M Agri LIFE Extension here is an article on Rabbiteye Blueberries which is very specific on the soil requirements for this plant. This article is emphatic that they will not grow in alkaline soils, which means that anyone in Central Texas, where the Wildflower Center, home of Mr. Smarty Plants, is located is out of luck. They demand acidic soils, which you probably have in Alabama. According to this USDA Plant Profile map, they do grow natively in Barbour County, which is right next to Russell and Lee Counties, and we can assume that the soils there are also appropriate soils. We suggest that you contact the Alabama Cooperative Extension System for Lee County for specific information on your soils.
Here is more information from Floridata, including that the Rabbiteye Blueberry does not tolerate clay or soggy soils.