They were actually at a manga cafe (if you read the tiny print at the end Taichi says "we can't ever go back to that manga cafe) manga cafes are setup as personal cubicles which of course have no ceiling, hence why he says "they can see us from above". I assume the person working there heard them and that's why he was so flustered. Hope I could help clarify the story some :)
Ohhh I see! I thought it was a camera due to the above since I guess that's where surveillance cameras are usually placed. I searched up some pictures and those cubicles seems to be very "opened" (?). Taichi really has no shame hahaha
The translation is a bit meh at some places, but I'm guessing there was a surveillance camera in the first chapter. Hence why Taichi moved the both of them, the receptionist getting flustered when he hands him back the cards and why he's saying they can't go there anymore at the end. Taichi really is a beast LOL