Rand could see Asmo through the window from his location in the Caemlyn Palace as well, before Asmo walked away to get wine. It's also explicitely told in the books that Slayer spies on people. When Slayer saw that Asmo went in a certain direction, he jumbed there via TAR (as said, Slayer most likely knows the Palace quite well) and had the luck that Asmo apparently opened the first door on his way. Thus Slayer got the perfect opportunity to kill Asmo, especially since the Palace was largely deserted at this time. If Asmo wouldn't have opened the door, Slayer had simply waited for another chance to get Asmo.

In my view that makes more sense than e.g. the idea that Graendal randomly wandered in this part of the Palace for some obscure reason and without any disguise.