I believe that the tiger came out of the door the young man opened, because:
Explanation:
It is said in the last part of the story that the Princess hates the lady that she knows is waiting behind that door, and she has been jealous of her before, the with the last question after all this explanation "Would it not be better for him to die at once, and go to wait for her in the blessed regions of semibarbaric futurity? " makes you think about the likelihood that she could have made her decision on base of that jealousy.
