Despite the importance of the Southern Ocean carbon sink, its response to future atmospheric CO2 perturbations and warming remains highly uncertain. In this study, we use six state-of-the-art Earth system models to assess the response of Southern Ocean air-sea CO2 fluxes (FCO2) to a rapid atmospheric forcing increase and subsequent negative emissions in an idealized carbon dioxide removal reversibility experiment. We find that during positive emissions, the region north of the Polar Front only takes up atmospheric CO2 for 30-50 years before reaching equilibrium; surface stratification and reduction of CO2 solubility with warming diminishes ocean CO2 uptake in this region. In contrast, south of the Polar Front, the upper ocean continues to take up CO2 until the end of positive emissions at 140 years. Sea-ice loss and the accumulation of anthropogenic dissolved inorganic carbon in the upper ocean reduce the upwelling-driven seasonal CO2 outgassing, leading to a stronger Antarctic CO2 sink. CO2 removal triggers a CO2 uptake reduction that slowly converts the Southern Ocean into a CO2 source which persists for at least 50 years post-mitigation. Furthermore, we find that model sensitivity to atmospheric perturbation is closely linked to seasonal FCO2 dynamics. Specifically, models with a thermally dominated pCO2 seasonal cycle exhibit nearly twice the sensitivity to atmospheric perturbations compared to non-thermal models. Our findings further emphasize the necessity of accurate model representation of the seasonal CO2 dynamics for appropriately simulating the future Southern Ocean carbon sink.