That Demandred at first controlled the Dragonsworn, who made much chaos (this fits with Sammael's comment about Demandred's friends in the south), and later additionally took Murandy to gather an army for the Shadow in the heart of the Westlands.

As an assassin we see Slayer several times strike at people, also at those formerly associated with the Shadow (like the BA or Fain). Therefore it's actually obvious that someone used him to kill Asmo (likely Graendal).