High-accuracy and high-timeliness efficient daily runoff simulation with strong explainability is essential for fine water resources management. However, existing single-station runoff simulation models struggle to meet basin-wide simultaneous scheduling and risk management demands due to insufficient consideration of nonstationarity, spatiotemporal dependencies, and multi-station interactions. In this paper, we propose a novel GVMD-PA-STGMD framework that integrates Variational Mode Decomposition with Grey Wolf Optimizer (GVMD), physics-aware methods (PA), and Spatiotemporal TCN-GNN-MHSA Deep-learning (STGMD) to improve multi-station daily runoff simulation in semi-arid areas. The STGMD model was developed by coupling Temporal Convolutional Network (TCN), Multi-Head Self-Attention (MHSA) and four Graph Neural Networks (GNNs) to capture spatiotemporal features of multi-station runoff. In particular, the multi-station Spatio-Temporal dependence matrices were innovatively proposed for explicitly characterizing spatial interactions and nonlinear temporal dependencies across hydrological stations, thereby improving the capability of GNNs. Meanwhile, two proposed physics-aware methods-multidimensional node characteristic and node decomposition methods were introduced to STGMD for extracting meteorological influences and reservoir regulation effects on runoff processes. Furthermore, we adopted GVMD into PA-STGMD models to decompose the multi-station nonstationary daily runoff into multiple relatively stationary sub-series for enhancing the stability of input data. Finally, the iterative gradient path integrated gradients (IG2) algorithm was employed for model explainability, while Adaptive Bandwidth Kernel Density Estimation (ABKDE) was used to provide the probabilistic interval simulation. Here, the proposed framework was validated by simulating multi-station daily runoff of Wei River, China. Results show that GVMD-PA-STGMD framework achieves the best performance, and GVMD-PA-STGMD3 in the framework show distinct improvements when compared to STGMD model in terms of both NSE (36.8%) and RMSE (48.7%), and improved NSE by 19.4% and RMSE by 42.3% over the PA-STGMD models. Additionally, compared with single-station models, the proposed framework not only achieves higher simulation accuracy but also maintains superior computational efficiency, improving simulation timeliness by 38.2%. Analyses from IG2 and ABKDE further confirm its strong explainability and low uncertainty. The study demonstrates that the proposed GVMD-PA-STGMD framework with a "multi-station Spatio-Temporal dependence matrices"-"physical awareness"-"non-stationary series decomposition"-"explainability analysis" modeling process is a promising approach, which enables accurate and computationally efficient non-stationary uncertainty daily runoff simulation with strong explainability and low uncertainty.