After St. Paul's appeal before Herod Agrippa II and Festus to state his case to Caesar in Rome, he was taken by a centurion of the Roman Imperial guard (Acts 27:1) to the harbor at Caesarea, where they found a ship of Adramyttium to convey them to Asia Minor. From Asia Minor, they anticipated finding another ship to Rome (27:6).
The contrary winds at Cyprus (27:4) were likely a foreshadowing that a Mediterranean storm was approaching. The storm system brought a fierce North-Easter the wind that brought down the boat they caught in Asia Minor, wrecking that ship.
The boat of Adramyttium was probably on the way back to her homeport, exchanging goods and passengers from Caesarea to Asia Minor, with several stops along the Aegean coast. It was likely that the Centurion Julius could find another boat to Rome from Asia Minor.