The rapid rise of social media platforms such as Twitter and Weibo has heightened the growing significance of crisis warning and situational awareness. The nature of bursts or events on these platforms has become more complex, as information spreads rapidly and unpredictably, often involving changes in time and location. Current research is insufficient in detecting these complex, evolving bursts, especially during the early stages of incidents. To address these challenges, we propose an Evolving Disaster Burst Detection (EBUD) framework over social streams, which enables early identification and tracking of bursts, facilitating quick response and decision-making. Specifically, we propose a novel Adaptive Entropy Distance based active learning strategy for user to label the most representative data, while the model is tasked with labelling the rest of the data, effectively improving the accuracy of data labelling. Finally, a two-stage sketch algorithm is proposed to monitor the frequency of each label in real-time, enabling swift detection of sudden surges that may signify emerging events. Comprehensive evaluations on social data streams have been carried out to show the effectiveness and efficiency of our proposed method.