There is an old joke: How can you tell if a person is from Oklahoma?
Answer: He is the one who stands outside in the thunderstorm looking at the sky.
Tornadoes can form quickly. During one warning, I stood outside and watched a funnel cloud form a mile away... it took 30 seconds. Luckily it also disappeared before it touched ground, but you get the idea.
The oldsters just ran to the shelters when the warnings hit (and our neighbors just put the kids into the shelter and left the door open to keep an eye on the sky.) One of my memories was trying to persuade Lolo to get into the neighbor's shelter (he wanted to put on his shoes and sock, not go in bedroom slippers). This was the middle of a hail storm, and the street was 4 inches deep in flowing water. We got him there with a minute to spare, but luckily the tornado hit a mile north of us so we were okay.
This CBS story asks why Tulsa's warning sirens didn't go off when a small tornado hit.
The officials said it was because by the time they got the radar warning, the tornado had moved on to Broken Arrow.
That sounds about right. Our sirens used to go off after the tornado had passed too, but in rural areas, you couldn't always rely on weather radios or the local media...we got our news from radio stations 30 miles to the east, 40 miles to the west, or 50 miles to the south. The best way to track what was going on was to check the local TV station for the map where the "warnings" were... a big problem if they hit at night.
However, for huge tornadoes, which don't look like funnel clouds, these warnings are life saving.
Since we had a couple of tornadoes nearby every year, you can see the problem: often folks don't pay attention to warnings and watches unless the local conditions suggest one is nearby.
So I'm so glad I now live in the Philippines, where we only have to worry about typhoons, floods, earthquakes, and dengue fever.