Modeling spatial-temporal interactions among neighboring agents is at the heart of multi-agent problems such as motion forecasting and crowd navigation. Despite notable progress, it remains unclear to which extent modern representations can capture the causal relationships behind agent interactions. In this work, we take an in-depth look at the causal awareness of these representations, from computational formalism to real-world practice. First, we revisit the notion of non-causal robustness studied in the recent CausalAgents benchmark. We show that existing representations are already partially resilient to perturbations of non-causal agents, and yet modeling indirect causal effects involving mediator agents remains challenging. To address this challenge, we introduce a metric learning approach that regularizes latent representations with causal annotations. Our controlled experiments show that this approach not only leads to higher degrees of causal awareness but also yields stronger out-of-distribution robustness. To further operationalize it in practice, we propose a sim-to-real causal transfer method via cross-domain multi-task learning. Experiments on trajectory prediction datasets show that our method can significantly boost generalization, even in the absence of real-world causal annotations, where we acquire higher prediction accuracy by only using 25% of real-world data. We hope our work provides a new perspective on the challenges and potential pathways toward causally-aware representations of multi-agent interactions. Our code is available in supplementary materials.