I recall an instance 4 or 5 years ago when the southbound Crescent was held at the Atlanta station about an hour because a tornado was on the ground about 30 miles from Atlanta. I was not present at the time but I was on the train about a week later and saw a lot of damage near the tracks.
I assume the passengers stayed on the train rather than herded into the station but I do not really know.
I recall seeing on the news 2 or 3 years ago when a tornado blew into downtown Nashville, TN., some footage shown where a freight train was stopped, at the far left of the screen, waiting for the storm to clear.
I also recall an instance when I was on MARTA(the subway system in ATL) and we were indeed escorted off the train to a downstairs area due to a possible nearby tornado.
I assume a train out in the middle of nowhere genuinely in the immediate path of a funnel would just stop, but I cannot thnk people would be herded into a basement, who would know where a nearby basement is?
If a tornado was just seen, at a distance, I assume the train would continue running normally. I guess it takes a judgement call by the conductor and seconded by the engineer.
Your question could not be more timely for me because we are in the middle of tornado warnings as I type, and have been 4 or 5 times the last week or two.