Tornadoes can strike in a variety of conditions, in any season.
You don't get to breath a sigh of relief when fall rolls around, because tornadoes can spin up under a variety of conditions.
While tornadoes are most common in the spring (and least common in the winter), they can also form in the fall. Both fall and spring are transitional periods where masses of warm and cool air are more likely to collide and create the thunderstorms that can spawn tornadoes.
Hurricanes can also spawn tornadoes as they hit coastal areas in the late summer and early fall.