This study addresses the problem of predicting the popularity evolution trends and inflection points of hot topics triggered by social emergencies. A method that integrates multimodal feature fusion and time-series modeling is proposed. First, multimodal features are constructed from the textual and visual content of posts, user influence, cascade propagation structures, temporal characteristics, and tag influence, after which a CatBoost model is used to estimate post-level popularity. Second, the post-level prediction results are aggregated into topic-level time series according to time windows to characterize the dynamic evolution characteristics of hot topics in terms of content, users, and propagation. Finally, an efficient S-Mamba model is introduced to predict the evolution trends of hot topics. Future key inflection points are predicted by integrating the E-Divisive method with slope and acceleration analyses. Experimental results on multiple real-world social media emergency datasets show that the proposed method outperforms various baseline models in both the accuracy and efficiency of inflection point prediction, while also maintaining high popularity prediction performance, verifying the effectiveness of multimodal feature construction and time-series modeling in hot topic inflection point prediction.