To my mind the answer is 'yes, but no'. Theories lie upon ontological and epistemological systems, but if you take Kuhn's notion of a paradigm seriously, those are not determined by philosophical ontology and epistemology, they are accepted by consensus (consciously or otherwise) to facilitate comparability between theories during the process of normal science. That means they take the form of theories themselves, even if those are often deeply suppressed assumptions. And they can be displaced by revolutionary science. But they need to be replace with an equally rigid structure before forward progress can really resume.
Ontology is responsible for determining what kinds of referents are allowed within a theory, and epistemology is responsible for limiting what kinds of relationships are worth being theorized about. Ideas beyond 'understanding' in whatever sense is current are not subjects of inquiry. Pursuing them would be pointless. A theory is any assertion within those boundaries. (Presuming riskless, unfalsifiable theories are still theories, just 'unscientific' ones.)
For example, one epistemological question that comes up occasionally: Does a theory involving unmediated action at a distance actually provide an understanding? Or is it too magical? Then do we need another understanding to explain such laws? If you hold onto that idea too hard, you can't tolerate the contributions of Newton or Bell. But it was a principle of Aristotelian physics, and relinquishing it bothered Newton deeply. Later it bothered Einstein. Only a revolutionary theory could dispense with it, so Newton dismissed his doubts. And a later revolution also gave it back. Now we have it again, in the form of the particles that underlie a field, and in the form of the curvature of space. If you can't embed your theory into those mechanisms, which both involve a sort of contact, it is not part of modern physics.
But that specific ontology and epistemology are simplified forms admitted by the science itself and enshrined in its operative paradigm. For instance, in physics, we have now decided everything must be communicated by a particle, that is our new ontology. (Particles are what exist. If we can't find the particle that delivers an effect directly, we need a different understanding in terms of other particles or their interactions.)
This kind of ontology is not comparable to philosophical ontology. It is purposely circumscribed to beautify the paradigm. It is also limited enough to threaten the theories built on it, if they pass certain bounds. If it allowed the whole scope of philosophical ontology, it could not be falsifiable, and should not be an attribute of a theory. (So not a part of the paradigm, which is a very general and vague, yet still scientific, theory.)
Likewise, each scientific paradigm delineates a specific, limited epistemology. There is a theory of causation implicitly or explicitly built into the underlying structure on which normal science proceeds. And the options for varying it are limited at another level by the choices of basic principles made by the science.
In the 17th century, you needed a contact-driven mechanism (even if that somehow involved God, with 'final cause' as a form of contact.) But we have changed the bases for our physics twice since then, and rearranged our notion of cause to fit quantum indeterminacy. Now, there can't be a cause that creates no observable correlation, for instance, or it is not a knowable cause. We cannot have a scientific understanding of the sequence of events. If a cause creates no correlations, it is beyond our expressive capacity, and cannot be understood by our process. So it is outside our limited, chosen, epistemology. Quantum theories with hidden processes that require the correlations be unobservable are dismissed. They cross outside the notion of cause we are using, creating spurious entities. (In addition they could not possibly be testable, at least at the necessary level of detail.)
But in the more general realm of philosophical epistemology, or even real life, we can reasonably imagine a cause that has its effect in so chaotic an environment that no correlation might be observed. We cannot determine 'butterfly effects' where tiny contributions overwhelm our capacity to see the cause of an effect. But we are fairly certain this is a thing that happens. The math makes it too likely. It just doesn't actually explain anything in a way that constitutes 'understanding'.
(Apologies for the length.)