Actually, until the era of the 1st World War, the practice on-board a ship was to call orders for the helmsman to actually move the "tiller", either to port or to starboard. So calling "hard a-port" meant moving the tiller to port, which means the rudder, and the vessel, will then move to starboard. With wheel steering, putting the helm/tiller to port, means spinning the wheel to starboard.
Ships no longer use this system - these days helm directions refer to the desired turn of the rudder/vessel.
The James Cameron movie The Titanic also contained a similar scene, which generated a lot of puzzlement. It IS a bit confusing at first, unless one is a sailor and is familiar with tiller steering.
Turning the wheel to starboard is not a mistake for the time period of the movie. The early tiller to wheel transitions resulted in the same change of rudder position. it is counter-intuitive today as most all boats with wheels now steer as a car does. Some sailboats still use the older method because of space and/or weight considerations.
Before the ferry is struck by the freighter, the captain of the ferry shouts "hard a-port", and the helmsman immediately starts turning the wheel to the right (starboard). In those days, the captain was directing which way to push the tiller or assembly, not the boat itself. see details below.