Damage from water pressure only applies to submerged areas.
This is explained in the Maelstrom: General Features section (emphasis mine):
Submerged areas are tinted blue from wall to wall. Characters who can’t breathe underwater must hold their breath in a submerged area. While submerged, they are also susceptible to the effect of water pressure.
The rules given for Water Pressure state emphasis mine):
Creatures and vehicles at Maelstrom’s depth take 7 (2d6) bludgeoning damage per minute from water pressure.
The rules require that you be both underwater and at the Maelstrom's depth to take this damage, and the map denotes these locations by tinting the entire room blue, wall to wall.1
This is close enough to consistent with real world physics.
You take damage while submerged at these depth because of the water pressure. If you aren't under water, there is no water pressure.
Pressure, whether air or water, is the weight of the column of air or water above you. When you are in a sealed underwater structure such as the Maelstrom, the roof of the structure is supporting that weight, so it is exerted on the structure, not on you, when you are inside the structure. To be fair, this isn’t exactly correct, as the maelstrom isn’t a sealed structure, but it’s close enough that for physics-minded people, suspension of belief shouldn’t be any more difficult for this than it is for magic.
I must add, the rules are not an attempt to simulate real world physics, but in this case, they do a decent enough job while keeping the game fun, given my somewhat hand waved explanation in the last paragraph.2
1 To be clear, I have not run Storm King's Thunder, but I have used the rules printed therein to build my own underwater locations.
2 In real life being at a depth of 3000 feet would definitely be fatal, though some theorize that it is possible using helium gas mixtures to prevent the nitrogen narcosis associated with the more common nitrogen-oxygen mixtures used by divers. Only five divers have ever gone below 1000 feet on scuba.