I think Bhaskar's main argument is that we have to presuppose the existence of objects or entities which exist independently of our knowing of them, in order to make sense of scientific or other forms of inquiry and activity. Bhaskar differentiates between the real, the actual, and the empirical, where the "real" is the irreducibility of objects to our knowledge of or about them; the "actual" is the events that are occurring at any given time (observed by us or not); and the "empirical" is our experience and interpretation of said events.
The "actuality" of any entity at any given time (its present manifestation) does not exhaust its being: dimensions of its (or our) being always remain unactualized, depending on the context. This is why it's necessary to do experiments or other forms of inquiry: what is actual at any given time, and present to experience at any given time, is not the "fullness" of that being; there is potential that is "out of phase" with the present and not manifest in the present context or set of relations. Our experiments and inquiry practices set the conditions to actualize what otherwise is not actualized (but nevertheless real). For Bhaskar, this means that both the actuality of a being and the empirical or experiential knowledge of this being must be differentiated from the reality of the being (which always exceeds and is irreducible to either).
In my understanding, Wilber is arguing that this amounts to saying that consciousness-free being comes first -- that entities exist wholly apart from consciousness -- and he sees this as a duplication of the old first-tier split between matter and mind. Wilber argues that reality is panpsychic -- that reality (following Whitehead) consists of prehensive experiential occasions, which co-create each other through their mutual prehensions. Wilber would agree that beings might exist or subsist independently of our (human) knowing of them, but they nevertheless do not exist independently of their prehension of each other.
In my reading of both Wilber and Bhaskar, I believe there is a slight misunderstanding here. (I might be wrong, but this is how I see it). Bhaskar embraces a kind of panpsychism (he thinks consciousness is "implicit" in things like atoms) and he also embraces nonduality, but he thinks we need to be careful about importing our anthropocentric notions of "experience" down to the level of atoms. But I don't think this is really a problem for Wilber, since Wilber clearly differentiates between prehension at the level of atoms or other simple holons and self-awareness at the human level. At any event, even with panpsychism embraced in both models (and Wilber's version is certainly stronger or more explicit), I think an important difference remains. In other words, the problem isn't so much the lack of panpsychism in Bhaskar (he admits a form of it), but how that is understood and how it is related to ontology. Wilber says that beings are not necessarily co-created by human agents, but they do co-create each other. I believe Bhaskar (or an OOO philosopher) would say that even for atoms or molecules or bacteria encountering each other, even if we grant that experience is always part of an actual occasion, and that it influences the actualization and the evolution of these beings in and through their interactions, the reality of beings cannot be reduced to or simply identified with their experience of each other or even their "actuality" at any given moment. There always remains an ontic depth "in the shadow," unmanifest, withdrawn from or exceeding present relations. From what I've read thus far, I'm not sure that Wilber has yet addressed this aspect of Bhaskar's argument.