Tornados can strike quickly and be deadly or not. We lived in Indiana most of our life and experienced more than we wanted. They are totally unpredictable. But we didn't live in fear that they might occur. . . just have a plan in the event they popped up.
Many parks and towns along the usual routes will have tornado shelters. Be familiar with them. When you check in, ask where the tornado shelter is. If they don't have one, move on or at least explore and see if there is anything available in the town.
In one park in Tye, Texas, it is a school bus buried in a hill, with only the back half visible. Rudimentary at best, but it would work. In Wisconsin we were told in the event of a tornado, head to the casino parking garage. I had not heard that before, but that would probably work.
Just be alert and don't drive into any storm. Be ready to adjust your travel if conditions don't look good. Unlike hurricanes which we know about several days in advance, they can only announce that "conditions are favorable" for a potential outbreak. Be safe, not sorry.
Dale