Understanding true influence in social media requires distinguishing correlation from causation--particularly when analyzing misinformation spread. While existing approaches focus on exposure metrics and network structures, they often fail to capture the causal mechanisms by which external temporal signals trigger engagement. We introduce a novel joint treatment-outcome framework that leverages existing sequential models to simultaneously adapt to both policy timing and engagement effects. Our approach adapts causal inference techniques from healthcare to estimate Average Treatment Effects (ATE) within the sequential nature of social media interactions, tackling challenges from external confounding signals. Through our experiments on real-world misinformation and disinformation datasets, we show that our models outperform existing benchmarks by 15--22% in predicting engagement across diverse counterfactual scenarios, including exposure adjustment, timing shifts, and varied intervention durations. Case studies on 492 social media users show our causal effect measure aligns strongly with the gold standard in influence estimation, the expert-based empirical influence.