Luc and Slayer are one being created/merged by the DO, Slayer enters TAR "in the flesh" (contrary to "in the dream" ), it makes sense that he can enter TAR in the flesh from everywhere in the Real World, consequently it also only makes sense that he can leave TAR at every place & return into the Real World (especially if he is an assassin, as e.g. the stanza about Slayer in the Dark Prophecy implies), this would actually also explain the strange assassination in the Stone and the WT, which apparently weren't done by a mere Gray Man, or why Fain's Myrddraal fears that much that Slayer will find it. It's a bit embarrassing that you still can't even grasp those simple basics, although I explained them several times.

I give you that probably only the deleted scene in TSR about Slayer's powers, which BS mentioned recently, would have made this blatantly obvious to many readers at that time . But as RJ said, he trusted that generally his readers are reasonable intelligent to deduce things and don't have to be told that water is wet.