In this work we presented a novel computational model of precipitation polymerization allowing one to obtain core-shell microgels via a realistic cross-linking process based on the experimental procedure. We showed that the cross-linker-monomer reactivity ratios r are responsible for the microgel internal structure. Values of r lower than 1 correspond to the case when alternating sequences occur at the early reaction stages; this leads to the formation of microgels with pronounced core-shell structure. The distribution of dangling ends for small values of r becomes bimodal with two well-distinguished peaks, which correspond to the core (short dangling ends) and corona (long dangling ends) regions. The density profiles confirm the existence of two distinct regions for small r: a densely cross-linked core and a loose corona entirely consisting of dangling ends with no cross-linker. The consumption of the cross-linker in the course in the microgel formation was found to be in a perfect agreement with the predictions of Monte Carlo (MC) model in the sequence space.