Some cousins live in tornado alley. What can they do to reassure their kids they will be ok while taking shelter during tornado warning?

Have a routine. Have "practice runs" to the shelter so it is more routine and "matter of fact" for the kids. Also have them have a favorite toy and games down there so it is not so intimidating.
Face this together. This is a little too close today. However, the thing that I do to reassure my family during tornadoes is to tell them that no matter what we are going to face the bad weather together. We are stronger as a family than we are individually. Then, we talk, laugh, sing, (and pray) together listening to weather reports until it is safe to come out.
Set a calm example. Kids only display behavior they witness, so act calm and don't make a big fuss and they will mirror your response to stress.
Safety /tornado. I would get a kids book a read about tornado's and how to provide safe havens during an event, then i would practice the steps needed to be taken during such an emergency a few times per year to provide reassurance to the kids.(just like we do fire drills in school) after awhile it becomes second nature. Good luck.