Most research into causal learning has focused on atemporal contingency data settings while fewer studies have examined learning and reasoning about systems exhibiting events that unfold in continuous time. Of these, none have yet explored learning about preventative causal influences. How do people use temporal information to infer which components of a causal system generate or prevent activity of other components? In what ways do generative and preventative causes interact in shaping the behavior of causal mechanisms and their learnability? Across three experiments, we explore human causal structure learning within a space of hypotheses that combine generative and preventative causal relationships. Participants observe the behavior of causal devices as they are perturbed by fixed interventions and subject to either regular or irregular spontaneous activations. We find that participants are robustly capable learners in this setting, successfully identifying the large majority of generative, preventative and non-causal relationships but making a few systematic errors. We develop a computational-level framework for normative inference in this setting and propose a family of algorithmic approximations. We find that participants judgment patterns can be well captured with a model that approximates normative inference via a simulation and summary statistics approximation scheme.