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Collaborative control of microgrid clusters is challenging due to their nested control structures and the integration of heterogeneous microgrids. Besides, the wide coverage also causes some remote and sensitive industrial loads to face degraded voltage levels in the cluster system. To tackle these challenges, this work develops a novel distributed control strategy for islanded microgrid clusters. The strategy introduces tracking differentiator technology to unify different inner dynamics in heterogeneous microgrids, making them able to be coordinated in the same distributed network. Additionally, to accurately maintain the voltage level of sensitive and remote loads during distributed coordination, a containment control scheme that designs the leaders based on the running bus states of selected loads is developed. This scheme can flexibly and accurately converge the bus states of selected loads and controlled microgrids into a predefined containment range. Furthermore, to prevent instability caused by extended buffer time, a prediction-based mechanism is proposed to compensate for asynchronous delays. Finally, the effectiveness of our strategy is validated through several simulation cases and an RTLAB-based experiment.