Do you think the rising action begins with Rainsford's fall from the ship, or does it begin later in the story when he finds out about the hunt?

One could argue that Rainsford accidentally falling off the yacht is the inciting incident and the beginning of the rising action of the story. An inciting incident occurs between the exposition and the rising action and is the moment when the action begins. The inciting incident is also referred to as the complication, which is essentially the catalyst that drives the plot of the story and gets the ball rolling. The rising action is the moment when the tension increases and is comprised of a series of conflicts leading to the climax. At the end of the exposition, Rainsford goes from relaxing on the top deck of the yacht to fighting for his life in the treacherous sea. Rainsford falling from the yacht significantly increases the tension and is the first conflict he faces in the story. Therefore, one could recognize the moment that Rainsford falls from the yacht as the inciting incident, which is the start of the rising action. When Rainsford discovers that General Zaroff is going to hunt him, it is simply another conflict in the rising action that continues to build until the climax.

Ultimately, this question is up to you.  I have seen both answers adequately defended.  In my person opinion, I believe that Rainford's fall from the ship is the start of the rising action.  
The inciting incident of a story is the point in a plot when an event or decision begins that story's problem. Everything before this moment is introductory backstory.  I believe that Rainsford's problem begins the moment that he must go to Zaroff's island.  That occurs when he falls off of the ship.  The rising action continues to rise as Rainsford realizes that Zaroff is trapping and hunting people.  The action continues to build until the story's ultimate climax.