Managed Multi-Context Systems (mMCSs) provide a general framework for integrating knowledge represented in heterogeneous KR formalisms. Recently, evolving Multi-Context Systems (eMCSs) have been introduced as an extension of mMCSs that add the ability to both react to, and reason in the presence of commonly temporary dynamic observations, and evolve by incorporating new knowledge. However, the general complexity of such an expressive formalism may simply be too high in cases where huge amounts of information have to be processed within a limited short amount of time, or even instantaneously. In this paper, we investigate under which conditions eMCSs may scale in such situations and we show that such polynomial eMCSs can be applied in a practical use case.