To add to Wyqvist’s good explanation:
The text for the objective should specify how close, at what max speed, and for how long. If not, the mission is faulty.
In addition, text will pop up alongside the objective telling you to get closer, reduce speed, etc.
There is also a countdown timer showing how long you need to wait.
Those advisory messages are generated automatically by the Uber condition that the creator uses to determine when the rescue is completed.
One characteristic of the Uber condition is that a
specific ship is called for—which the swimmer will follow if it is close enough.
Therefore the player does not have a choice of ship or deployable to use. The ship or boat should be specified in the objective text if there is more than one that the player might choose.