When the earthquake shakes the soil laterally, than the foundation moves with the soil. The seismic waves then are transferred throughout the structure over time as the seismic wave travels up to the structure. The base isolator is there and it reduces the stiffness of the structure. This way it lowers the natural frequency and the building’s superstructure will respond to the vibrations as a rigid unit instead of resonating with the vibrations. 
Actually, the building’s foundation moves with the ground while the base isolator flexes to reduce the motion of the ground from affecting the superstructure” (superstructure is demonstrated in Figure 4). The images are presenting the way the bildings move in those seconds whan the earthquake is happening. Take a look!
