The production of high-quality liquid/liquid emulsions is a key factor in many industrial processes, such as in food or pharmaceutical industries. The premix emulsification process enables the controlled adjustment of fine and narrow distributed droplet sizes. Furthermore, premix emulsification in porous structures is considered a low-shear process that enables the usage and formulation of shear sensitive media (e.g., proteins). However, the local and time-dependent stress conditions and stress residence time at the droplet interface during droplet dispersion in micro-porous structures are still unknown. In this paper, interfacial stress distributions during droplet dispersion in premix membrane emulsification are numerically (computational fluid dynamics, CFD) investigated. Time-dependent stress conditions and stress residence times at the interface are calculated. The stress conditions are related to the droplet deformation process to identify the main mechanisms for droplet breakup. The results are compared to experimental analysis of the resulting droplet size distribution during emulsion formulation. It has been found that higher shear stresses occur at the pore wall, but lower shear stresses at the liquid/liquid (disperse/continuous) interface are responsible for the droplet dispersion process. The stress residence time shows that lower stresses are present over a longer time compared to higher stresses. This is relevant for the understanding of the dispersion process, but also for the use of shear sensitive media (e.g., proteins as emulsifier).