Big Data architectures allow to flexibly store and process heterogeneous data, from multiple sources, in their original format. The structure of those data, commonly supplied by means of REST APIs, is continuously evolving. Thus data analysts need to adapt their analytical processes after each API release. This gets more challenging when performing an integrated or historical analysis. To cope with such complexity, in this paper, we present the Big Data Integration ontology, the core construct to govern the data integration process under schema evolution by systematically annotating it with information regarding the schema of the sources. We present a query rewriting algorithm that, using the annotated ontology, converts queries posed over the ontology to queries over the sources. To cope with syntactic evolution in the sources, we present an algorithm that semi-automatically adapts the ontology upon new releases. This guarantees ontology-mediated queries to correctly retrieve data from the most recent schema version as well as correctness in historical queries. A functional and performance evaluation on real-world APIs is performed to validate our approach.