Seems hard to believe that it was clear skies, given the obvious clouds. Storms don't form and spawn tornadoes in the time it takes to land and taxi clear; the system had to have been visible plainly and on radar.
Another aircraft lands (downwind) right behind the citation as the camera is bouncing around and shipping containers are tumbling into view. Basic airmanship might suggest a more prudent approach, like diverting.
A rope twister formed near an airport where I was working last year. We had a fire call about the same time, or just before. It didn't take a lot of watching the weather to refuse the flight, and shortly after that, we were filming a tornado. Certainly tornadoes can develop quickly, but they don't come from nowhere. It's also best if everyone in the area is prepared by not flying near such convective conditions in the first place.