Being in the heart of tornado alley, my biggest advice is to pay attention to what the locals say and do. If the locals are not overly concerned, you will probably be ok. The problem with the NOAA weather alerts is that they are for too wide of an area. Tornados are highly localized, i.e. if a tornado is 1/2 mile away and not coming at you, you are fine. Plus they typically are on the ground for only a few minutes (maybe a couple of miles or so). If you watch a local TV weather report, only when the "Tornado Warning" box is flashing on the weather map do you worry. They used to use the term Tornado Alert to signify the same thing but for some reason, that is no longer used. Anyway, a flashing box means an actual tornado has been either spotted by an official or by weather radar using tell-tale signatures. Plus, at least here in Oklahoma, they can spot a tornado on radar within a half mile so if the TV report says on is on the ground 5 miles away, you are probably fine so long as the storm cell is not headed toward you. TV reports also give the ETA of the storm to very specific areas so it helps to know the name (or nickname) of the area you are in.
If a tornado is imminent, take cover in a slow spot. Do not take shelter in a mobile home (I swear they have tornado magnets in them), RV, or other less-sturdy structure. If at a campground, a bathroom is usually a pretty good choice as they are frequently made out of cinder blocks and contain lots of small "rooms" without windows.
Also, in the day time, if you see a green sky (yep, green), take immediate cover as that means a pretty severe hail storm is very close by. Note that hail can easily come without a green sky but if a green sky, you got hail and plenty of it. To me, hail is the most likely to cause some serious damage. Nickel-sized hail will shred a tent. Baseball size hail (usually in KS, NE, SD, IA) can easily kill.
Most weather related scared I have been was in Wyoming decades ago in July. I was somewhere northwest of Dubois and I was camping at a campground up on a ridge with no trees. Middle of the night a ferocious lightning storm came up. Lots of booms at the same time as the flash (means lightning is REALLY close) nearby. Probably lasted about 10 minutes but boy was I scared. I kept wondering if my little aluminum tent poles would act either as a lightning rod or disperse a strike.
I personally love a strong thunderstorm as it shows the power of Mother Nature, so long as no one is hurt of course.
Tailwinds, John