After the island explodes, the sea is perfectly calm. A huge eruption like that would have produced a huge tsunami.
Going into a cave would not protect anyone from the smoke of a fire. The cave would fill will smoke as the fire progressed. And it would be slow to clear.
The movie uses the old quicksand (mudpit) trope - where someone goes in and soon disappears underneath when unable to get out. Time and again that has been shown to be false. People can merely become stuck, but they do not sink completely. Death if it comes from such circumstances is from the very slow consequences of becoming stuck there - thirst, starvation, exposure, an incoming tide etc.
In the scenes in the village during one eruption, the ground splits. The trench into which the loose soil falls to create this effect can be seen even before the dirt disappears.
At approximately one hour and 48 minutes into the film, when a convict falls into a mud pit and drowns, just before he disappears below the surface you can see a mistake in the background matte which shows the volcano. The glaring mistake reveals part of the background appearing in front of the top of his head, making it appear as though the top of his head is missing. Then as he slips further down, the top of his head then comes back into view as his head falls below the matte.
When one of the convicts has fallen in the mud pit, a bald headed man in dark clothing (crew member) can be seen behind the fauna to the right, pulling him with a rope further from rescue from Frank Sinatra's character.
When trying to rescue one of the convicts from the mud pit, Frank Sinatra wastes time tying a rope around himself first, to safely go in after him. - instead of just quickly throwing the end of the rope to the convict in order to haul him out.