The online spread of rumours in disasters can create panic and anxiety and disrupt crisis operations. Hence, it is crucial to take measure against such a distressing phenomenon since it can turn into a crisis by itself. In this work, the automatic rumour detection in natural disasters is addressed from an imbalanced learning perspective due to the rumour dearth versus non-rumour abundance in social networks. We first provide two datasets by collecting and annotating tweets regarding the Hurricane Florence and Kerala flood. We then capture the properties of rumours and non-rumours in those disasters using 83 theory-based and early-available features, 47 of which are proposed for the first time. The proposed features show a high discrimination power that help us distinguish rumours from non-rumours more reliably. Next, We build the rumour identification models using imbalanced learning to address the scarcity of rumours compared to non-rumour. Additionally, to replicate the rumour detection in the real-world situation, we practice cross-incident learning by training the classifier with the samples of one incident and test it with the other one. In the end we measure the impact of imbalanced learning using Bayesian Wilcoxon Signed-rank test and observe a significant improvement in the classifiers performance.