Free-electron laser based x-ray facilities require high-brightness photoinjectors to provide low emittance electron beams at a fixed bunch charge. The emittance optimization in the injector determines the lowest achievable emittance. Based on experimental emittance optimization at the photoinjector test facility at DESY in Zeuthen, a space-charge affected emission regime is identified, in which the optimum transverse beam emittance is achieved and thus, the injector is routinely operated in this regime. An advanced modeling approach is proposed to consider a dynamic emission process in the simulation of injector beam dynamics, meanwhile allowing detailed studies of the impact of strong space-charge fields during emission on the slice formation of the emitted electron bunch at the cathode. As an application, the proposed approach is used to analyze the budget of the optimized transverse beam emittance. An interplay, taking place in the identified emission regime, between intrinsic cathode emittance and space-charge induced emittance is demonstrated. The resolved behavior by simulation is consistent with the corresponding measurement under practical operation conditions of interest. The obtained results are reported.