Why does tomato soup "explode" when boiled?
I think it's probably a combination of things you mention. First, tomato soup is a suspension of solids (tomato tissue) in water. So it's the water that's boiling. That water is turning into steam, which bubbles out of the water. The solid suspension likely traps some of that steam until the pressure builds and you get a big explosive bubble.

I happen to cook, and make a fair bit of tomato sauce, which is very similar to tomato soup. I disagree with your statement that tomato soup explodes only once upon boiling. I see bubbles popping quite continuously, and you have to stir often to prevent this. Which happens to also be the way you prevent bumping in laboratory conditions. Cooking is probably the most comparable chemistry application most people are exposed to.