This work presents a Monte Carlo analysis of the propagation of correlation strength in site-bond square lattices generated through the dual site-bond model (DSBM), where the values of the property assigned to sites and bonds are sampled from two uniform density distributions that may have some overlapping area with each other. Correlations appear when a construction principle is established. Although this model has been extensively used in many physical applications, such as adsorption and surface diffusion on heterogeneous surfaces and percolation and transport processes in porous media, a careful study of the way correlated topology is settled on through the system was lacking. The dependence of the relaxation time needed to reach equilibrium and of the minimum size of the network to be used is established for different correlation strengths, represented by the overlapping parameter Ohm. A more accurate empirical equation, relating the characteristic correlation length Eo, corresponding to the spatial correlation function, and Ohm, is found, than the one used in former applications of the DSBM.