Hybrid-electric aircraft represent an important step in the transition from conventional fuel-based propulsion to fully-electric aircraft. For hybrid power systems, overall aircraft performance and efficiency highly depend on the coordination of the fuel and electrical systems and the ability to effectively control state and input trajectories at the limits of safe operation. In such a safety-critical application, the chosen control strategy must ensure the closed-loop system adheres to these operational limits. While hierarchical Model Predictive Control (MPC) has proven to be a computationally efficient approach to coordinated control of complex systems across multiple timescales, most formulations are not supported by theoretical guarantees of actuator and state constraint satisfaction. To provide guaranteed constraint satisfaction, this paper presents set-based hierarchical MPC of a 16 state hybrid-electric aircraft power system. Within the proposed two-level vertical hierarchy, the long-term control decisions of the upper-level controller and the short-term control decisions of the lower-level controller are coordinated through the use of waysets. Simulation results show the benefits of this coordination in the context of hybrid-electric aircraft performance and demonstrate the practicality of applying set-based hierarchical MPC to complex multi-timescale systems.