During emergencies, affected people use social media platforms for interaction and collaboration. Social media is used to ask for help, provide moral support, and to help each other, without direct face-to-face interactions. From a social presence point of view, we analyzed Twitter messages to understand how people cooperate and collaborate with each other during heavy rains and subsequent floods in Chennai, India. We conducted a manual content analysis to build social presence classifiers comprising intimacy and immediacy concepts which we used to train a machine learning approach to subsequently analyze the whole dataset of 1.65 million tweets. The results showed that the majority of the immediacy tweets are conveying the needs and urgencies of affected people requesting for help. We argue that during disasters, the online social presence creates a sense of responsibility and common identity among the social media users to participate in relief activities.