This study proposes Structural Gating and Effect-aligned Discovery for Temporal Causal Discovery (SGED-TCD), a novel and general framework for lag-resolved causal discovery in complex multivariate time series. SGED-TCD combines explicit structural gating, stability-oriented learning, perturbation-effect alignment, and unified graph extraction to improve the interpretability, robustness, and functional consistency of inferred causal graphs. To evaluate its effectiveness in a representative real-world setting, we apply SGED-TCD to teleconnection-driven compound heatwave--air-pollution extremes in eastern and northern China. Using large-scale climate indices, regional circulation and boundary-layer variables, and compound extreme indicators, the framework reconstructs weighted causal networks with explicit dominant lags and relative causal importance. The inferred networks reveal clear regional and seasonal heterogeneity: warm-season extremes in Eastern China are mainly linked to low-latitude oceanic variability through circulation, radiation, and ventilation pathways, whereas cold-season extremes in Northern China are more strongly governed by high-latitude circulation variability associated with boundary-layer suppression and persistent stagnation. These results show that SGED-TCD can recover physically interpretable, hierarchical, and lag-resolved causal pathways in a challenging climate--environment system. More broadly, the proposed framework is not restricted to the present application and provides a general basis for temporal causal discovery in other complex domains.