The Fatui is quite a large organization and always a few steps ahead of the Traveler. In some quests, wherever you are going, Fatui members are already in that area and go against the Traveler to get their work done. Enemies like Treasure hoarders aren't much of a deal because they are not as organized and vast as the fatui are. Also, one unique thing about the Fatui is that Her Majesty, the Tsaritsa, exercises absolute control over them, and her words are final. You learn about her and how Fatui members see her as a god. She is the cryo archon and has selected influential individuals named Harbingers to fulfill her wishes. We are yet to know more about them and have only seen three harbingers so far. All of those three, Childe, Scaramouche, and Signora, were cunning, smart, and powerful in their own ways. I'm excited to see how other members will be revealed later in the story and how they will influence the plot.