Back to the OP's question, when the sirens sound, my inclination is a hybrid of the bail out and run through the rain option and Herk's "load the TV and get ready to roll" option. I have absolutely no desire to get caught in the camper in high winds, let alone a tornado.
Had our first occasion to make the call in April of this year when camping at Van Buren State Park in South Haven, Michigan. It was around mid-day, raining, and we were huddled in the TT eating while I watched the radar. I noted what appeared to be a hook echo out over Lake Michigan what amounted to about 15 miles pretty much due west of us. Decided it looked like that little storm was going to slide by us, though, and told my wife, son, DIL, and daughter I thought we should be ok. Two minutes later, sirens! Immediately ordered everyone to the cars, and they were all loaded (with a 3 year old and two infants) in about 1 minute flat. We ran out and jumped in the cars while I dialed the park office. As we started the cars and our convoy began rolling out of the CG, the ranger answered the phone and said the sirens were from the nearby nuclear power plant and part of an extended emergency systems testing they do once each month.
The CG was mostly empty (it was early April), but we were the only campsite out of about 20 which was evacuated. People sat at their picnic tables (sirens blaring) and watched us run, load, and roll.
I'm sure nobody knew what the sirens were, they just all hung out at their campsites wondering what was up.
Don't just set there folks. Have a drill!
2013 Windjammer 3008W
2006 Chevy Silverado 2500HD 6.0L w/Equalizer 4
Nights camped: 2012 (29); 2013 (26); 2014 (40); 2015 (43); 2016 (35)