Multi-Robot Task Allocation (MRTA) with spatiotemporal constraints presents significant challenges in environmental adaptability. Existing learning-based methods often overlook environmental spatial constraints, leading to spatial information distortion. To address this, we formulate the problem as an asynchronous Markov Decision Process over a directed heterogeneous graph and propose a novel heterogeneous graph neural network named the Edge-Enhanced Attention Network (E2AN). This network integrates a specialized encoder, the Edge-Enhanced Heterogeneous Graph Attention Network (E2HGAT), with an attention-based decoder. By incorporating edge attributes to effectively characterize path costs under spatial constraints, E2HGAT corrects spatial distortion. Furthermore, our approach supports flexible extension to diverse payload scenarios via node attribute adaptation. Extensive experiments conducted in simulated environments with obstructed maps demonstrate that the proposed method outperforms baseline algorithms in task success rate. Remarkably, the model maintains its advantages in generalization tests on unseen maps as well as in scalability tests across varying problem sizes. Ablation studies further validate the critical role of the proposed encoder in capturing spatiotemporal dependencies. Additionally, real-time performance analysis confirms the method’s feasibility for online deployment. Overall, this study offers an effective solution for MRTA problems with complex constraints.