If you recall the events of Hyoukyo Mirror, you might remember that Shiori always knows what's going on around the school - and so Taku figures that it wouldn't hurt to try and ask her about the occult club. Even if the club was long gone when Shiori entered Soumei High, there's still a chance she might have heard something. He just didn't expect her to remember so dang fast!

Comic transcript

He turns around and interrupts Shiori's monologue.

Taku: "Hey... Have you ever heard of an occult club at our school? It was most likely closed down a few years ago."

Taken aback by the sudden change of topic, she gets a bit confused.

Shiori: "Y-Yeah?"
Taku: "Do you recall any of the members then?"
Shiori: "Umm..."
Taku: "Like some guy with a big scar on his face, or another one with piercing red eyes-"
Shiori: "Wait, wait! Let me think about it for a moment..."

She ponders only for a moment before perking up right away, a metaphorical lightbulb flashing above her head.

Shiori: "Aha! Got it!!"
Taku: "Wow, that was fast!?"