I used to storm chase when younger and have seen EXTENSIVE damage but also just a block away, absolutely nothing wrong. Bring a small (pack of cards size) radio (does not need to a weather radio) and listen to the forecast. If it is going to be bad, get a motel or head away from it (harder with dog if you can only travel 20 miles max per day). I have never heard of a touring cyclist killed by a tornado, but I have seen a bike struck by lightening before (awesome, scared the !@#$ out of us), and leaves a little weld mark).
Use reasonable common sense and you should be fine.