In this paper, we present detailed simulations with asymmetric initial beam settings in the context of the proposed Future Circular Collider e+e- (FCC-ee) using the xsuite framework. We compare simulated equilibrium bunch sizes and luminosities against an already existing analytical model, which shows remarkably good agreement for realistic small perturbations. We investigate the longitudinal top-up injection, the currently preferred injection scheme for the FCC-ee, using self-consistent simulations featuring beam-beam collisions with beamstrahlung and the injection process for the first time. We present and assess the sensitivity and required precision of the nominal beam parameters in a potential real-life operation by providing first estimates of the tolerances in the initial asymmetry of several machine parameters, with respect to the 3D flip-flop mechanism, obtained from parameter scan simulations.