Current approaches for modeling propagation in networks (e.g., spread of disease) are unable to adequately capture temporal properties of the data such as order and duration of evolving connections or dynamic likelihoods of propagation along these connections. Temporal models in evolving networks are crucial in many applications that need to analyze dynamic spread. For example, a disease-spreading virus has varying transmissibility based on interactions between individuals occurring over time with different frequency, proximity, and venue population density. To capture such behaviors, we first develop the Temporal Independent Cascade (T-IC) model and propose a novel spread function, that we prove to be submodular, with a hypergraph-based sampling strategy that efficiently utilizes dynamic propagation probabilities. We then introduce the notion of 'reverse spread' using the proposed T-IC processes, and develop solutions to identify both sentinel/detector nodes and highly susceptible nodes. The proven guarantees of approximation quality enable scalable analysis of highly granular temporal networks. Extensive experimental results on a variety of real-world datasets show that the proposed approach significantly outperforms the alternatives in modeling both if and how spread occurs, by considering evolving network topology as well as granular contact/interaction information. Our approach has numerous applications, including its utility for the vital challenge of monitoring disease spread. Utilizing the proposed methods and T-IC, we analyze the impact of various intervention strategies over real spatio-temporal contact networks. Our approach is shown also to be highly effective in quantifying the importance of superspreaders, designing targeted restrictions for controlling spread, and backward contact tracing.