I'm giving a nod to simplicity here: Slayer was ordered to hunt Rand because everyone had orders to do the same. Even darkfriends with none of his powers made attempts on his life. Being able to actually attack a channeler who is standing near you, ready to defend themselves is a different matter from a surprise assassination attempt.

Semirhage, for example, was wounded because she stopped paying attention to Min and focused on Rand. The two Black Ajah were killed while Shielded - and the indication is that they were weaker than Asmodean was anyway, since Asmodean could teach Rand a number of weaves requiring a certain level of strength.

No member of the Dark had any idea that Asmodean had not voluntarily allied with Rand; their assumption was that he was at full strength, and that makes him more than a match for Slayer. Even at partial strength, he was more than a match for Slayer. Heck, even in Tel'Aran'Rhiod he was more than a match for Slayer. It would actually be easier to defeat and destroy Slayer in T'A'R for an Age of Legends channeler than in the real world due to their training.

For simplicity's sake, this is what I think would happen: Slayer steps out of T'A'R. Asmodean channels saidin, seizes Slayer with Air and then incinerates him with Fire.

After all, in the same time it took Asmodean to say "You? No!" he could have had all manner of protective weaves in front of him. It really doesn't take that long.