Spatiotemporal reachability queries arise naturally when determining how diseases, information, physical items can propagate through a collection of moving objects; such queries are significant for many important domains like epidemiology, public health, security monitoring, surveillance, and social networks. While traditional reachability queries have been studied in graphs extensively, what makes spatiotemporal reachability queries different and challenging is that the associated graph is dynamic and space-time dependent. As the spatiotemporal dataset becomes very large over time, a solution needs to be I/O-efficient. Previous work assumes an ‘instant exchange’ scenario (where information can be instantly transferred and retransmitted between objects), which may not be the case in many real world applications. In this paper we propose the RICC (Reachability Index Construction by Contraction) approach for processing spatiotemporal reachability queries without the instant exchange assumption. We tested our algorithm on two types of realistic datasets using queries of various temporal lengths and different types (with single and multiple sources and targets). The results of our experiments show that RICC can be efficiently used for answering a wide range of spatiotemporal reachability queries on disk-resident datasets.