The active hero takes 1 damage if the Young Vampire is on either one of the 2 tiles that comprises the Start tile.
Exactly. Per the rules (available here: http://www.wizards.com/dnd/files/Castle_Ravenloft_RuleBook.p...), Page 5, under the heading Dungeon Tile Stack: "The Start Tile is where the Heroes usually enter the dungeon and begin their adventure. It is twice the size of other tiles." The part I emphasized is the key wording that describes "Start Tile" and anything you see/read that refers to the "Start Tile." In other words, it's the entire piece.
The only time you count the Start Tile as two individual tiles (hence the line that bisects it) is explained here (same page and heading as above): "The Start tile actually consists of two separate tiles that are already connected; treat each as its own tile for the purposes of movement and counting tiles."
So, since the Young Vampire's tactic refers to the words "Start tile" then we used the entire piece.