Since RJ said that one should read closely, I want to analyse Asmo's last moments in TFoH in detail:
"He pulled open a small door, intending to find his way to the pantry. There should be some decent wine. One step, and he stopped, the blood draining from his face. “You? No!” The word still hung in the air when death took him."

After Asmo went for a short while (maybe at least one minute, considering all his thoughts and that he was without any hurry) leaving Mat & Aviendha at the fountain in the garden, he comes to a wall in front of him with a long balefire gash and finally, after maybe at least another minute, reaches a closed small door, which leads to an unknown location. He pulls the door open, which takes him probably at least one second. When he opens the door, he doesn't immediately see his killer, though. He still thinks about wine. Then Asmo takes one step into the room/corridor behind the door. This probably also takes at least one second. Then Asmo suddenly stops, because he surprisingly sees not too far away a person he didn't expect there, recognizes this person & becomes immediately scared. To realize all this probably also takes at least one second for Asmo. Either the person was hidden behind the door, so that Asmo couldn't already see the person, when he opened the door, or the person suddenly appeared before him in this moment (like e.g. Slayer does). Then Asmo addresses the killer with the question "you?", which probably takes at least another second. Then the killer uses a quick weapon (either a prepared OP weave, an aimed crossbow or knife) to kill Asmo in likely one second, so that Asmo can only say "no!", when he sees the weapon hitting him, because only the word "no!" still hung in the air, when death took him. There are no other witnesses around and Asmo's body was either destroyed by a OP weave or the killer brought it away. Another detail is that Asmo apparently had his harp in his hands oder under his arm, which might have made it a bit more difficult for him to react quickly to counter an attack (e.g. if he needs his hands to perform a OP weave).

Since Asmo spent some minutes with Mat and Aviendha before he left them, it's possible that the killer spied on Asmo for some time (like Rand watches Asmo playing the harp at the fountain from his window in the first floor), and figured where he would probably go. Thus, the killer might have been able to enter the room/corridor before Asmo at the moment, when Asmo makes his step into the room (especially if the killer knows the Caemlyn palace very well like e.g. Luc probably does).

I would definitely say that the killer was better prepared to quickly fight/kill someone than Asmo was, since Asmo was without any hurry, had idle thoughts before, was then suddenly surprised, scared and had his harp in the hands to hinder him a bit.

This is my basic interpretation of the scene and its timing. Agreements or disagreements?