@Kaji not really. He's not behaving in this manner because of their deal surrounding exclusivity, but because he's emotionally invested in their relationship and jealous. Since their deal was "no attachments", he's getting stressed over his own conditions, and has no security around the permanency of their relationship. He's yet to realise his feelings, so he grasps onto straws like "we had a deal, but you're sleeping around" when that's not the case at all, he just doesn't like being second to someone recognised as a close companion
Himefujo at your service