Scenario 20 - when is the end of my turn?
Ah, the joys of trying to thrash reasonable and consistent rules out of Betrayal at House on the Hill.  Let me give it a shot.

The answer is probably either 2 or 3.  I'd lean towards 2.

The basic rulebook has this to say about turns during the Haunt:


  Haunt Turn Order
  The first turn always starts with the player to the traitor’s
  left and goes clockwise (further away from the traitor). Each
  of the heroes gets a hero turn. After each hero has had a
  turn, the traitor gets his or her traitor turn. After the traitor’s
  turn, any monsters controlled by the traitor get a monster
  turn. (One player gets two turns: one for the traitor and one
  for the monsters.)


(I've found two versions of the rulebook so far.  The wording differed slightly between the two, but not materially in this section)

This clarifies two things: The traitor's turn and the monster's turn are considered separate turns, and both of those turns are considered to belong to the traitor player.

So, the big question then becomes, did the Traitor's Tome mean "you" the traitor, or "you" the player?  The rules are (of course) rather vague, but I'm pretty sure they mean "you" the traitor.

For evidence, I turn to Haunt 30, Tomb of Dracula


   In Tomb of Dracula the traitor controls monsters (vampires), and uses the turn tracker.  Specifically, the turn tracker related rules are thus:

 
 [Setup]
 Set up the Turn/Damage track with a plastic clip at 0.  You'll use it to keep track of time

 You Must Do This...
 ... at the start of your turn.  Advance the Turn/Damage track to the next number, beginning with 1.

 Vampires
 Dracula needs time to awaken.  He doesn't move or attack normally until Turn 2 (he can still defend against attacks.)
 

 Now, if the Turn marker is advanced at the beginning of both the Traitor and Monster turns, then Turn 2 is reached on the first Monster turn, which means that Dracula wouldn't actually have any downtime.  Clearly, this is not what is intended, so clearly "At the start of your turn" means "At the start of the traitor's turn" for this Haunt.


Given that "At the start of your turn" almost certainly means "At the start of the traitor's turn" for Haunt 30, I think that it's reasonable that "At the end of each of your turns" means "At the end of each of the traitor's turns" for Haunt 20.

On a more philosophical level, having the turn tracker advance once per round is more logical to me than having it advance once for the traitor and once for the monsters.  Since my philosophical intuition, and my rules-based inferences match up, I'm going to go with that.