"Stay in a safe place" image from the Fire and Disaster Management Agency (Japan)
Even in a basin as small as the Mediterranean, tsunamis can last for many hours, and the first waves can be followed by bigger ones. Until the Civil Protection Authorities issue the end-of-event message, stay in the safe area indicated in your municipality's civil protection plan. Do not go back to the coast under any circumstance: bigger and more dangerous waves may come. Do not return home unless explicitly authorised by Civil Protection officials and follow their instructions to understand what to do and when to leave the place where you are.In the meantime, ensure the health of the people around you and, if possible, provide first aid. During an emergency, telephone lines are very important for assessing damage and coordinating rescue operations. Only use the telephone for real needs: excessive telephone traffic can seriously limit the operation of the networks and thus the effectiveness of rescue operations.After a tsunami, do not drink tap water and do not eat food that has come into contact with the water and materials transported by the tsunami: they could be contaminated.
More information on the Civil Protection website.