Short answer: yes, they do
It is true that pressure increases with depth, and so zero depth implies zero pressure. But you have to consider the fact that if the liquid has air above (like the ocean does) then it will have pressure at the surface due to the depth of the air above it. This pressure must be equal to the atmospheric pressure at that point. Some physics questions ignore this air pressure and only focus on pressure from the liquid, but the extra pressure due to air pressure is always there in reality (unless the fluid is in a vacuum).
It's also intuitively obvious using Newton's laws that a fluid must exert pressure on the air above it, because for example if the ocean did not exerted an upwards force on the atmosphere, then the net force on the ocean would be downwards, which due to Newton's 2nd law would imply that the surface of the water would accelerate downwards, which makes no sense. Obviously the water is in equilibrium, so it must be exerting a force to counteract the pressure from the atmosphere.