During quiet times in between earthquakes (interseismic periods), the oceanic crust is slowly pulled under the continental crust (at about 2 inches/year, the speed fingernails grow). There are places where the plates stick together (locked) and places where they don't (creeping).
At locked zones, the lower plate pulls the upper plate down with it, causing the island to sink (though at 2 inches/year it is nearly imperceptible).
Stress at the locked zone builds.
When the stress becomes too great, the upper plate breaks free and springs back, causing the island to suddenly pop up, an earthquake, and a tsunami.
This "seismic cycle" recurs about every 250 years.