After run-up, part of the tsunami energy is reflected back to the open ocean. In addition, a tsunami can generate a particular type of wave called edge waves that travel back-and forth, parallel to shore.

These effects result in many arrivals of the tsunami at a particular point on the coast rather than a single wave suggested by the picture in amplification phase.

Citation source: http://www.owlnet.rice.edu/~esci108/108_EQ_Lec_4.ppt

Source of picture: http://www.nature.com/news/2004/041229/full/041229-4.html