Called it. He spilled his spaghetti (unable to talk and and walked with a long awkward silence), flubbed the sudden pasta convo AND dropped the ball by talking about another girl, making Yukihira think he wanted to walk home with Miyahara. Triple kill.
Rei wants to talk more with him with just them both, but I don't think it's because she's falling in love. At least not right now. She's probably more into shipping them and enjoys hearing more stories about how they get along so well. Or perhaps worse for him, maybe she's into Miyahara...