Datasets involving irregular occurrences of different types of events over the timeline are increasingly commonly available. Proximal graphical event models (PGEMs) are a recent graphical representation for modeling relationships between different event types in such datasets. Existing algorithms for learning PGEMs from event datasets perform poorly on the task of structure discovery, which is particularly important for causal inference since the underlying graph determines the effect of interventions. In this paper, we explore causal semantics in PGEMs and study process independencies implied by the graphical structure of the model. We introduce (conditional) process independence tests for causal PGEMs, deploying them using variations of constraint-based structure discovery algorithms for Bayesian networks. Through experiments with synthetic and real datasets, we show that the proposed approaches are better at balancing precision and recall, demonstrating improved F1 scores over state-of-the-art baselines.