It's cute how she made the effort to reach and pat him over the counter, but I hope nobody caught a glimpse under that short skirt of hers at that moment. I can almost hear Izumi's heart sink like a stone dropped in a pool after page 1.
On a more serious note, did he actually do a joyful shout at the counter? That could've disturbed customers and gotten him a reprimand from the manager. I mean, he works at what is practically a private library with extra amenities like food, drinks and even showers. Fine, let's just handwave it as dead hours with few customers around in the manga cafe and the manager on a smoke break or something.
What if her big sister is one of his professors at uni, or maybe even his thesis advisor? That could be interesting.