Modeling the asymmetric transmission of geopolitical shocks across structurally diverse emerging markets presents a severe computational challenge. Traditional homogeneous deep learning approaches often suffer from negative transfer and base-rate bias when applied to cross-country financial prediction. To address this, we propose the Heterogeneous Multi-Task Spatiotemporal Network (HMT-STN), a structurally adaptive framework that integrates country-specific embeddings, heterogeneous task decoupling, and a Focal Loss mechanism. Evaluated on a daily panel dataset of ASEAN-4 equity markets (2016–2026), the HMT-STN is designed to simultaneously optimize directional return classification and volatility regression. Comprehensive evaluations using Precision, Recall, F1-score, and AUC-ROC demonstrate the framework's superior discriminative power, notably achieving 66.21% accuracy and an AUC-ROC of 0.68 in Thailand, a highly volatile transitional market. Rigorous ablation studies confirm that Focal Loss prevents catastrophic performance collapse in noisy environments, while country embeddings successfully isolate market-specific idiosyncrasies. Furthermore, SHAP (SHapley Additive exPlanations) analysis reveals a tripartite spectrum of cross-country heterogeneity, providing model-based feature attributions that are consistent with established economic theories of market segmentation and geopolitical risk sensitivity. Collectively, this study demonstrates that explicitly modeling cross-country heterogeneity through heterogeneous multi-task learning offers a robust, interpretable, and computationally efficient paradigm for geopolitical risk assessment in fragmented global economies.