A traditional modal realist, which is a possibilist, would assume that all and only possible worlds are real worlds that exist and that an impossible world is an existing world that is not real. By "existing", I mean "being" in the Kantian sense of specifying particulars pertaining to particular domains of discourse (or universes of objects). Therein, modal realism does not preclude Meinong's Jungle, which is a domain of discourse in which impossible things exist, but before getting to that it is important to establish some foundation.
Perhaps not ironically, your question is a modal question. "Do impossible worlds have to be incorporated in some way if one maintains he/she is a modal realist?" means to ask (as a modal realist), "Are impossible worlds possible worlds?" Answering "yes" seems to pose a contradiction, but the question is not specific enough. "Impossible real worlds are possible real worlds" is a contradiction and "impossible real worlds are possible unreal worlds" is not. That is, if "R" stands for "real world" such that ¬R denotes "unreal world" then ¬◇R∧◇R is a contradiction and ¬◇R∧◇¬R is a tautology.
Much of modern ways of thinking about the metaphysics of modality can be traced back to Leibniz, and Leibniz associated impossibility with contradiction. For him, contradictions were impossible combinations such that, for any ontology, the only necessarily false statements were contradictory statements. To be more specific, necessitatem absolutum, in Leibnizian philosophy, entails truth in all possible worlds by virtue of principium contradictionis. “Les vérités nécessaires sont fondées sur le principe de contradiction” (Leibniz 1686). Likewise, impossibility entails falsity in every possible world, which justifies principium exclusi tertii sive medii inter duo contradictori. “In like manner as […] an assertion cannot be both true and false, so […] an assertion must be either true or false” (Mill 1843).
Meinong's Jungle can be regarded as the singular unreal world, the only impossible world, and the sole world wherein there are unreal things like 4-vertice triangles.
Whereas the actualism-possibilism debate is one about whether or not non-actual real things are possible, your question reduces to a question about whether or not impossible things are real.
Necessitatem absolutum ought not to be confused with necessitatem ex hypothesi. “Necessity […] consists either in the constant conjunction of like objects, or in the inference of the understating from one object to another” (Hume 1748). Necessitatem ex hypothesi is the truth/falsity of an apodosis as being contingently necessary for the truth/falsity of any hypothesis to which that apodosis belongs (irrespective of any protasis in particular). On the other hand, necessitatem absolutum may invoke a Parmenideanistic mundus intelligibilis (perhaps evocative of Platonic-Pythagorean εἶδοη). “Indépendamment de la preuve qu'on appelle apodictique [il y a donc] une certitude que nous avons souvent [...] qualifier de philosophique ou de rationelle, parce qu'elle résulte d'un jugement de la raison” (Cournot 1851).