Hi Adb2, I guess what you have to remember is that an erupting volcano is a very different thing from a fire, even though they might be similar-looking. As you probably know, fire is a chemical reaction that requires oxygen to keep going. If you put a fire under water you remove the source of oxygen and the reaction stops.
Eruptions are very different though.
However, this doesn't mean that underwater eruptions are identical to those on dry land. Water can have very strong influences on the characteristics of an eruption, but mainly because it is the water itself that gets converted to steam which then explodes. This happens only if the water is shallow because deep water is under enough pressure to prevent explosive steam production. If anything, these magma-water interactions act to make eruptions MORE explosive rather than less explosive. I hope that helps to answer your question.