Living in the southern end of tornado alley all my 70 years I can tell you be aware but not worried. In that time I have seen 3 and the last one of any significance at all to hit our town was in 1948. Although tornados are extremely destructive, they actually do damage in relatively small areas. Typically they are in the range of 1/4 mile wide and stay on the ground for only a few miles. That amounts to a very tiny fraction of the land area. Obviously some are much larger. Of course none of that matters if you happen to be caught in the path of one.
Check local forecast daily. If storms are forecast, check several times daily. Have a good radar on your smart phone. Don't drive into a storm in your path. Stop and let it pass. When you stop for the night, ask if the RV park has a storm shelter or designated safe area. If not ask where the nearest safe area may be. If there are no better options nearby and a severe storm is approaching then go to a nearby large Walmart, Home Depot, lowes, or similar store. They typically have areas designated for their employees and customers to go in that event. Don't stay in the RV or car or truck if in the path of a tornado.