Spatiotemporal activity modeling is an important task for applications like tour recommendation and place search. The recently developed geographical topic models have demonstrated compelling results in using geo-Tagged social media (GTSM) for spatiotemporal activity modeling. Nevertheless, they all operate in batch and cannot dynamically accommodate the latest information in the GTSM stream to reveal up-To-date spatiotemporal activities. We propose ReAct, a method that processes continuous GTSM streams and obtains recency-Aware spatiotemporal activity models on the fly. Distinguished from existing topic-based methods, ReAct embeds all the regions, hours, and keywords into the same latent space to capture their correlations. To generate high-quality embeddings, it adopts a novel semi-supervised multimodal embedding paradigm that leverages the activity category information to guide the embedding process. Furthermore, as new records arrive continuously, it employs strategies to effectively incorporate the new information while preserving the knowledge encoded in previous embeddings. Our experiments on the geo-Tagged tweet streams in two major cities have shown that ReAct significantly outperforms existing methods for location and activity retrieval tasks.