First, I'm guessing these happen because of a weather machine somewhere?

Second, is there anything you can do apart from standing around giving them food and switching places trying to keep them out of the way?

Might make them more frequent, but you are right, they happen when there isn't a weather machine, or even one under construction.

One game I had, I think, 5 tornadoes, maybe 6, and in one case, I had no more than gated down, spent a couple seconds looking at the map to see where I was headed, when another touched down. And spending time on that meant enough of a delay that both the Warmaster and Apothecary were booted out of town for crimes against the city.

My take-away is that aggressive civil defense measures against natural disasters is a bad idea. ;)

Ya, when a weather machine gets built I basically drop everything and get to it or the town will be toast soon. It takes way too much time to babysit and heal the town leaders every time a tornado touches down...

Tornadoes are probably what have lost me the most towns.