The Oxford English Dictionary - the 'bible' in such matters - offers the following as the opening words for a definition of 'under'...
"in senses denoting position, beneath or below something, so as to have it above or overhead or TO BE COVERED BY IT."
There is no doubt but that a submerged submarine is "covered by" the sea. In simpler terms, 'under' actually just means "below the surface", in any case, as in "He could swim a length under the water." If we wrote, 'in the water' there, it would just mean 'on the surface'.