According to an analysis of tornadoes by ENSO phase, a year with a La Niña present is more likely to have tornadoes in northern and western parts of the Southeast, while a year with an El Niño is likely to have more tornadoes in southern Alabama, Georgia and Florida.  Since we are currently in a weak La Niña, that would tend to favor more tornado activity in northern Alabama and the Carolinas and less in Georgia, southern Alabama and Florida, although the effect would be limited due to the weakness of La Niña.

You can also see this in the map of when fatal tornadoes occur, with blue lines representing La Niña storms.  Of course, tornadoes in the Southeast can and do happen any month of the year, so it is important to pay attention to weather forecasts for the possibility of severe weather through the seasons.