So to make sure I understand, the moment a player takes the booty tile of their choice, they also at that very moment, bring in their character into the den?
Essentially, yes. At dusk, you take a booty tile, and carry out its special action if it's a saber or Spanish Officer. Then you place your character card in your den (unless you took a Spanish Officer).
Then the next player takes their dusk actions.
(Note that you don't take a booty tile if there are none left or if you played the Cabin Boy, but of course you still place your character card in your den.)