Sparknotes' commentary for On the Quai at Smyrna seems to have quite a few historical errors. The commentary states that the narrator is likely talking about the Greek evacuation of Thrace, but the title is On the Quai at Smyrna. Smyrna is a city in modern-day Turkey (now called Izmir). The Christian (mainly Greek and Armenian) part of Smyrna was burned in 1922 after the Turks recaptured the city from the Greeks. Hemingway was actually in Turkey just after the Great Fire to cover the Greco-Turkish War as a correspondent for the Toronto Star.
Also, the Ottoman Empire (modern-day Turkey) was actually not an ally of the United States in World War I. The United States was one of the Allied Powers (or the Triple Entente) and the Ottoman Empire was one of the Central Powers that fought against the Triple Entente.
However, the Great Fire of Smyrna occurred in 1922, after World War I was already over. The Great Fire occurred towards the end of the Greco-Turkish war. Even if the event referred to had been the evacuation of Thrace, that event also occurred in 1922. The Allied ships were in Smyrna to guard their own diplomatic compounds as the transfer of power occurred. They were under orders to remain neutral, however, and therefore did not rescue the Greek and Armenian refugees.