Graphs provide a powerful basis for modeling Web-based relational data, with expressive GNNs to support the effective learning in dynamic web environments. However, real-world deployment is hindered by pervasive out-of-distribution (OOD) shifts, where evolving user activity and changing content semantics alter feature distributions and labeling criteria. These shifts often lead to unstable or overconfident predictions, undermining the trustworthiness required for Web4Good applications. Achieving reliable OOD generalization demands principled and interpretable uncertainty estimation; however, existing methods are largely post-hoc, insensitive to distribution shifts, and unable to explain where uncertainty arises especially in high-stakes settings. To address these limitations, we introduce SpIking GrapH predicTive coding (SIGHT), an uncertainty-aware plug-in graph learning module for reliable OOD Generalization. SIGHT performs iterative, error-driven correction over spiking graph states, enabling models to expose internal mismatch signals that reveal where predictions become unreliable. Across multiple graph benchmarks and diverse OOD scenarios, SIGHT consistently enhances predictive accuracy, uncertainty estimation, and interpretability when integrated with GNNs.