The Pierre Auger Observatory is currently upgrading its surface detector array by placing a 3.84 square meter scintillator on top of 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 extensive air showers, which ultimately facilitates reconstruction of the mass composition of ultra-high-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 presented in addition to the tuning of these simulations to detector response measurements performed using a centimeter precision muon telescope. Augmentations of the Offline framework in order to accommodate the large-scale detector upgrade are also presented.