Effective dynamic scheduling of twin Automated Stacking Cranes (ASCs) is essential for improving the efficiency of automated storage yards. While Deep Reinforcement Learning (DRL) has shown promise in a variety of scheduling problems, the dynamic twin ASCs scheduling problem is challenging owing to its unique attributes, including the dynamic arrival of containers, sequence-dependent setup and potential ASC interference. A novel DRL method is proposed in this paper to minimize the ASC run time and traffic congestion in the yard. Considering the information interference from ineligible containers, dynamic masked self-attention (DMA) is designed to capture the location-related relationship between containers. Additionally, we propose local information complementary attention (LICA) to supplement congestion-related information for decision making. The embeddings grasped by the LICA-DMA neural architecture can effectively represent the system state. Extensive experiments show that the agent can learn high-quality scheduling policies. Compared with rule-based heuristics, the learned policies have significantly better performance with reasonable time costs. The policies also exhibit impressive generalization ability in unseen scenarios with various scales or distributions.