Correlation does not always equal causation. It seems to me that a wet fall and or winter is a sign of an active jet stream across the Southern U.S. so it stands to reason that such a pattern will linger into the Spring before breaking down if it's going to do so. Thus more rain days equal more storm days and thus more "opportunities" for tornadoes. If you are in a high pressure ridge pattern over the South keeping the jet stream storm track further North and West, then logically this creates drought and if you are in a winter drought it too will likely linger into the Spring before the pattern breaks down if it is going to do so. Drought means less rain storms which means less severe storms thus logically fewer "opportunities" for tornadoes.  Here is the abstract and the link to the full research online.

A seasonal-scale climatological analysis correlating spring tornadic activity with antecedent fall-winter drought in the southeastern United States

Marshall Shepherd¹, Dev Niyogi² and Thomas L Mote¹

¹ Climate Research Laboratory, Department of Geography, University of Georgia, Athens, GA 30602, USA
² Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907, USA

Received 10 February 2009
Accepted 16 June 2009
Published 24 June 2009

Abstract. Using rain gauge and satellite-based rainfall climatologies and the NOAA Storm Prediction Center tornado database (1952-2007), this study found a statistically significant tendency for fall-winter drought conditions to be correlated with below-normal tornado days the following spring in north Georgia (i.e. 93% of the years) and other regions of the Southeast. Non-drought years had nearly twice as many tornado days in the study area as drought years and were also five to six times more likely to have multiple tornado days. Individual tornadic events are largely a function of the convective-mesoscale thermodynamic and dynamic environments, thus the study does not attempt to overstate predictability. Yet, the results may provide seasonal guidance in an analogous manner to the well known Sahelian rainfall and Cape Verde hurricane activity relationships.  UGA drought-tornado relationship research paper