The location profiles of social media users are valuable for various applications, such as marketing and real-world analysis. As most users do not disclose their home locations, the problem of inferring home locations has been well studied in recent years. In fact, most existing methods perform batch inference using static (i.e., pre-stored) social media contents. However, social media contents are generated and delivered in real-time as social streams. In this situation, it is important to continuously update current inference results based on the newly arriving contents to improve the results over time. Moreover, it is effective for location inference to use the spatiotemporal correlation between contents and locations. The main idea of this paper is that we can infer the locations of users who simultaneously post about a local event (e.g., earthquakes). Hence, in this paper, we propose an online location inference method over social streams that exploits the spatiotemporal correlation, achieving 1) continuous updates with low computational and storage costs, and 2) better inference accuracy than that of existing methods. The experimental results using a Twitter dataset show that our method reduces the inference error to less than 68% of existing methods. The results also show that the proposed method can update inference results in constant time regardless of the amount of accumulated contents.