Inferring causal relationships between event pairs in a temporal sequence is applicable in many domains such as healthcare, manufacturing, and transportation. Most existing work on causal inference primarily focuses on event types within the designated domain, without considering the impact of exogenous out-of-domain interventions. In real-world settings, these out-of-domain interventions can significantly alter causal dynamics. To address this gap, we propose a new causal framework to define average treatment effect (ATE), beyond independent and identically distributed (i.i.d.) data in classic Rubin’s causal framework, to capture the causal relation shift between events of temporal process under out-of-domain intervention. We design an unbiased ATE estimator, and devise a Transformer-based neural network model to handle both long-range temporal dependencies and local patterns while integrating out-of-domain intervention information into process modeling. Extensive experiments on both simulated and real-world datasets demonstrate that our method outperforms baselines in ATE estimation and goodness-of-fit under out-of-domain-augmented point processes. The supplementary materials are available here .