The core challenge in basketball tactic modeling lies in efficiently extracting complex spatial-temporal dependencies from historical data and accurately predicting various in-game events. Existing state-of-the-art (SOTA) models, primarily based on graph neural networks (GNNs), encounter difficulties in capturing long-term, long-distance, and fine-grained interactions among heterogeneous player nodes, as well as in recognizing interaction patterns. Additionally, they exhibit limited generalization to untrained downstream tasks and zero-shot scenarios. In this work, we propose a Spatial-Temporal Propagation Symmetry-Aware Graph Transformer for fine-grained game modeling. This architecture explicitly captures delay effects in the spatial space to enhance player node representations across discrete-time slices, employing symmetry-invariant priors to guide the attention mechanism. We also introduce an efficient contrastive learning strategy to train a Mixture of Tactics Experts module, facilitating differentiated modeling of offensive tactics. By integrating dense training with sparse inference, we achieve a 2.4x improvement in model efficiency. Moreover, the incorporation of Lightweight Graph Grounding for Large Language Models enables robust performance in open-ended downstream tasks and zero-shot scenarios, including novel teams or players. The proposed model, TacticExpert, delineates a vertically integrated large model framework for basketball, unifying pretraining across multiple datasets and downstream prediction tasks. Fine-grained modeling modules significantly enhance spatial-temporal representations, and visualization analyzes confirm the strong interpretability of the model.