In open environments, agents need to reason with knowledge from various sources, possibly represented in different languages. The framework of Multi-Context Systems (MCSs) offers an expressive, yet flexible, solution since it allows for the integration of knowledge from different heterogeneous sources in an effective and modular way. However, MCSs are essentially static as they were not designed for dynamic scenarios. The recently introduced evolving Multi-Context Systems (eMCSs) extend MCSs by also allowing the system to both react to, and reason in the presence of dynamic observations, and evolve by incorporating new knowledge, thus making it even more adequate in Multi-Agent Systems characterised by their dynamic and open nature. In dynamic scenarios which admit several possible alternative evolutions, the notion of minimal change has always played a crucial role in determining the most plausible choice. However, different KR formalisms - as combined within eMCSs - may require different notions of minimal change, making their study and their interplay a relevant highly nontrivial problem. In this paper, we study the notion of minimal change in eMCSs, by presenting and discussing alternative minimal change criteria.