Data trees, typically encoded in JSON, are ubiquitous in data-driven applications. This ubiquity makes urgent the development of novel techniques for querying heterogeneous JSON data in a flexible manner. We propose a rule language for JSON, called constrained tree-rules, whose purpose is to provide a high-level unified view of heterogeneous JSON data and infer implicit information. As reasoning with constrained tree-rules is undecidable, we identify a relevant subset featuring tractable query answering, for which we design an automata-based query rewriting algorithm. Our approach consists of leveraging NoSQL document stores by means of a novel instance-aware query-rewriting technique. We present an extensive experimental analysis on large collections of several million JSON records. Our results show the importance of instance-aware rewriting as well as the efficiency and scalability of our approach.