Accurate traffic forecasting is crucial for intelligent transportation systems but remains challenging due to four fundamental problems: (1) multi-scale spatial dependencies where traffic exhibits hierarchical correlations from local intersections to city-wide flows, (2) non-stationary temporal patterns influenced by external factors and temporal context, (3) distribution shift and robustness issues caused by sensor failures, topological changes, and traffic regime shifts, and (4) adaptive multi-modal fusion requiring context-aware integration of spatial, temporal, and external features. To address these challenges, we propose MAST-Net, a Manifold-constrained Adaptive Spatio-Temporal Network that integrates spatial, temporal, and external features through three core innovations: (1) a manifold-preserving learnable augmentation module that adapts regularisation intensity to traffic regimes, providing provable bounds on distribution shift under explicit smoothness assumptions; (2) a parallel multi-scale graph convolution that achieves computational efficiency while maintaining representational power; and (3) a temporal-consistency-constrained meta-knowledge integrator with Lipschitz guarantees ensuring smooth prediction evolution. Under the assumptions of manifold smoothness and bounded data distribution, our theoretical analysis establishes generalisation bounds and robustness guarantees under real-world perturbations. Extensive experiments on four benchmark datasets demonstrate that MAST-Net consistently outperforms state-of-the-art methods across all prediction horizons, with ablation studies confirming the contribution of each architectural innovation. This work provides a robust and adaptable solution for real-world traffic forecasting, with theoretical results that hold under specified conditions empirically validated on the datasets considered. The implementation code is publicly available at https://github.com/afofanah/MAST-Net to ensure reproducibility.