I have watched the news when tornadoes are in the area, in Lindale. The local Tyler station would interrupt regular broadcasting to track tornadoes in real time. We were on satellite TV. We were in a doublewide with no tornado shelter. Watching a tornado drawing nearer and the TV would go out. Do we get in the car and make a run for it? Do we bend over and kiss our a$$ goodbye? What a quandary. We never got hit by a tornado, we never made a run for safety. Eh.
We were in a restaurant in Lindale once when a tornado hit town. The restaurant manager wanted everyone in the kitchen. I'm looking at giant bubbling pots of all kinds of stuff that could make some third degree burns if sloshed all over a person, thinking that was a bad idea. My husband was at the windows, typical redneck style, looking for the tornado. A friend an hour away was on the phone with me, tracking the tornado. The tornado came down and tore up a dollar store, used car lot and went merrily on it's way out of town towards our area. When we started home, we followed the damage. There was a tree leaned over the road that almost scraped the cab of the truck, but we got under it. We didn't know if we would have a home left, but it was unscathed.
I live in what is called locally, tornado alley. Some areas are more prone to tornadoes than others. About 15 miles from me is a swath of dead topped pine trees from a tornado some 9 years ago, That one went through a small town called Alto and tore up some homes and the school. No one was hurt. But it mostly went through the forest. I've lived along the coastal area most of my life in hurricane country. Hurricanes also spawn tornadoes. I think a tornado came down our street in hurricane Ike as trees were toppled, power line poles twisted off and it laid a massive oak tree on our house.
If your new home is in a tornado alley, the locals will know it and can tell you. But they can show up anywhere like unwanted guests. I think Texas leads the nation for tornadoes. You have a basement, a safe place. If a tornado shows up, you may only have time to get yourself in it. Trying to catch cats, whose senses would be going wild at that point, might not be a good idea. Outside dogs would just have to be on their own, an inside dog might join you. Safety for you first. In towns, there are tornado sirens. Out in the country, not so much. The TV might stop regular broadcasting to track tornadoes, but if it is at night, you wouldn't know it. How far is your bedroom from the basement entrance? How fast can you get there? If you sleep in your birthday suit, you might want to put a couple sets of clothing in the basement, along with shoes. Forget trying to grab anything, just get to the basement.
You currently live with earthquakes. Those show up with no warning. You also live in a state famous for it's fires. Fires take everything in it's path. Every area has its dangers. If I were you, I wouldn't stress over a tornado any more than you stress over an earthquake. Make your preparations and stop worrying about it.