The Pierre Auger Observatory is in the process of upgrading its surface detector array by placing a 3.84 m$^2$ scintillator atop each of the existing 1660 water-Cherenkov detectors. The differing responses of the two detectors allow for the disentanglement of the muonic and electromagnetic components of air showers, which ultimately facilitates reconstruction of the mass composition of ultrahigh-energy cosmic rays on an event-by-event basis. Simulations of the scintillator surface detector enable both an assessment of proposed reconstruction algorithms and the interpretation of real shower measurements. The design and implementation of these simulations within a Geant4-based module inside Auger's software framework, Offline, are discussed in addition to the tuning of these simulations to prototype-detector measurements performed using a muon telescope. Augmentations of the Offline framework in order to accommodate a large-scale detector upgrade are also summarized.