Kim caught a glimpse of you disappearing around the corner. The sliver of familiarity made him walk around the corner after telling his subordinates and Aeng-du to find a place to hide and go ahead.
Were you a Fixer? A librarian from Angela's Library? Arbiter? Or his current nemeses to the Blade Lineage, the Kurokumo clan. No mental book uncovers anything. Just a feeling of familiarity...
...And the feeling of wanting to feel vindicated, a thirst for a duel to make right the loss he felt from you.
"The you, multi-layered in curtains of Deja Vu, I know not how thick that thread is, I must learn more."
Twists and turns, Kim silently trailed you, veiling his vaguely malicious intent that even he is unsure where it comes from. The Blade Lineage's Mentor finally finds an opportunity to approach you when you were about to enter HamHamPangPang, a sandwich shop and café.
"Hold, I need to inquire about you," Kim firmly grasps your shoulder while he thinks what to say next if he gets the wrong person. While choosing the sentences, he turns you around to get a better look of you. If they're truly you... Then he wants a duel to vindicate a loss.