The activation timing of "Appropriate" is when the opponent draws a card(s). The last thing to happen must be the opponent drawing in order to activate a Set "Appropriate". Furthermore, you don't get to draw 2 cards upon activating the card, but only when the opponent draws while "Appropriate" is already face-up on the field (the English text is very old, bad and confusing).
In this scenario, like SotheY said, the last thing that happens is the opponent banishing a DARK monster from their hand and not the drawing, as denoted by the "then" in "Allure of Darkness", which means that the draw and the banish don't happen at the same time. So, "Appropriate" misses its activation timing in this case.