Many ICT applications need to make sense of large volumes of streaming data to detect situations of interest and enable timely reactions. The Stream Reasoning (SR) domain aims to combine the performance of stream/event processing and the reasoning expressiveness of knowledge representation systems by adopting Semantic Web standards to represent streaming elements. In this paper, we argue that the mainstream SR model is not flexible enough to properly express the temporal relations common in many applications. We show that the model can miss relevant information and lead to inconsistent derivations. Moving from these premises, we introduce a novel SR model that provides expressive ontological and temporal reasoning by neatly decoupling their scope to avoid information loss and inconsistency. We implement the model in the DOTR system that defines ontological reasoning using Datalog and temporal reasoning using the TESLA Complex Event Processing language, which builds on metric temporal logic. We demonstrate the expressiveness of our model through various examples and benchmarks. We also show that DOTR outperforms state-of-the-art SR tools.