This paper presents the application of Hierarchical Model Predictive Control (HMPC) as an energy management framework for a multi-timescale mixed-energy system, i.e., Power-to-X (PtX). The goal of the energy managing controller is to minimize an economic objective by determining the energy flows within the system. HMPC enables a long-term scheduling solution to anticipate ahead of the seasonal energy mismatches occurring in PtX systems. This paper presents a novel approach to couple the separate control layers in the hierarchy by heuristic assignment to fully employ the PtX fundamentals in the controller design. Simulation results based on historical data of the Dutch energy sector show the suitability of HMPC and its superiority over a rule-based control approach. The proposed controller may, however, also be used for any configuration of multi-timescale mixed-energy systems dealing with temporal energy mismatches.