The mountain offers no seal. At Palawan's Puerto Princesa Underground River, ocean tides reach kilometers inland because the cave channel remains connected to the sea, allowing changes in coastal water level to travel beneath the limestone roof. Rock conceals the connection. What looks like an isolated underground river is, along its lower reaches, an estuary.
The opening matters more. Limestone dissolves when rainwater, made weakly acidic by dissolved carbon dioxide, seeps through fractures and gradually enlarges them into passages through a process called karstification. The sea inherits that plumbing. When the tide rises, higher water at the river mouth changes the hydraulic gradient, reducing the river's seaward slope and transmitting a water-level disturbance upstream through the connected channel. Flow can slow or reverse. As the tide falls, the coastal water level drops, and freshwater draining from the catchment can discharge more readily toward the sea.
Distance can mislead here. A tidal rise detected kilometers inside does not mean that the same parcel of seawater has traveled the entire distance, because a water-level signal can propagate beyond the strongest saltwater intrusion. Salt tells another story. Denser seawater can move beneath freshwater, while turbulence mixes the layers; rainfall, river discharge and passage geometry determine how far that salt penetrates and how strongly tides register inland. The distinction defeats the apparent paradox. Beneath the mountain, the river surface rises and falls with a sea that remains out of sight.