Coordinating large teams of heterogeneous mobile agents to perform complex tasks efficiently has scalability bottlenecks in feasible and optimal task scheduling, with critical applications in logistics, manufacturing, and disaster response. Existing task allocation and scheduling methods, including heuristics and optimization-based solvers, often fail to scale and overlook inter-task dependencies and agent heterogeneity. We propose a novel Simultaneous Decision-Making model for Heterogeneous Multi-Agent Task Allocation and Scheduling (HM-MATAS), built on a Residual Heterogeneous Graph Transformer with edge and node-level attention. Our model encodes agent capabilities, travel times, and temporospatial constraints into a rich graph representation and is trainable via reinforcement learning. Trained on small-scale problems (10 agents, 20 tasks), our model generalizes effectively to significantly larger scenarios (up to 40 agents and 200 tasks), enabling fast, one-shot task assignment and scheduling. Our simultaneous model outperforms classical heuristics by assigning 164.10\% more feasible tasks given temporal constraints in 3.83\% of the time, metaheuristics by 201.54\% in 0.01\% of the time and exact solver by 231.73\% in 0.03\% of the time, while achieving $20\times$-to-$250\times$ speedup from prior graph-based methods across scales.