Pellet Rules and Jena Rules are Very Different™
The short answer is that Pellet supports SWRL rules. If you have an ontology that contains SWRL rules and ask Pellet to reason over it, it will take them into consideration.
Jena has its own rules language, which is described in the documentation page, Reasoners and rule engines: Jena inference support. It supports both forward and backward chaining rules.
However, though both Pellet and Jena support a notion of rules, the intended domains of SWRL rules and Jena rules are very different. SWRL rules are OWL-level constructs; the unary predicates in a SWRL rule are class expressions, and the binary predicates are object and data properties. Additionally, SWRL rules only match on named individuals; they don't match for individuals whose existence is only inferred. Jena rules, on the other hand, are RDF-level, and designed to work on RDF-graphs. While RDF and OWL are often used together, (e.g., OWL data is serialized in RDF), the two are conceptually distinct. An OWL reasoner could be implemented that makes no use of RDF, and a SWRL engine could be built that make no use of RDF graphs.
Jena or OWL API?
The code that you've shown, based on the presence of an OWLOntologyManager, is based on the OWL API, not on Jena's API. The OWL API will have more direct functionality for working with OWL and SWRL rules, while Jena will not. (Jena's OntModels work well with OWL1, but support for OWL2 is not complete (and still “open for contributors”).
Rather than using the OWL API or trying to use Jena's API, you'll probably find it easier to create rules using an editor such as Protégé. Martin Kuba has written a very nice OWL2 and SWRL Tutorial that can help you here.