As global demand for green hydrogen rises, potential hydrogen exporters move into the spotlight. While exports can bring countries revenue, large-scale on-grid hydrogen electrolysis for export can profoundly impact domestic energy prices and energy-related emissions. Our investigation explores the interplay of hydrogen exports, domestic energy transition and temporal hydrogen regulation, employing a sector-coupled energy model in Morocco. We find substantial co-benefits of domestic carbon dioxide mitigation and hydrogen exports, whereby exports can reduce market-based costs for domestic electricity consumers while mitigation reduces costs for hydrogen exporters. However, increasing hydrogen exports in a fossil-dominated system can substantially raise market-based costs for domestic electricity consumers, but surprisingly, temporal matching of hydrogen production can lower these costs by up to 31% with minimal impact on exporters. Here, we show that this policy instrument can steer the welfare (re-)distribution between hydrogen exporting firms, hydrogen importers, and domestic electricity consumers and hereby increases acceptance among actors.