Understanding the dynamical evolution of a percolating network during liquid–liquid demixing is crucial for many technological applications, including plastic electronics, such as organic photovoltaics, whose performance depends on the efficiency to transport the positive and negative charge carriers to the corresponding electrodes. The transport and collection of the charge carriers require sufficient asymmetry between the donor and acceptor phases by attaining a minimum concentration of the majority fluids in it, called the percolation threshold. We investigate demixing in symmetric binary blends on a substrate preferentially wet by one of the fluids from the perspective of such a percolation threshold to achieve directed and connectivity percolation. We also study the influence of the strength of the substrate interaction and the property of the blend right before the quench with respect to the critical point. It is commonly assumed that the bicontinuous morphology of a symmetric blend guarantees percolation, where the average concentration of the blend distinguishes the two phases. However, if the percolation threshold is larger than the average concentration, we find that percolating pathways grow monotonically and a percolating cluster forms only after a time lag. Furthermore, we find that this time lag is characterized by two universal kinetic regimes that can explain all our observations. The first regime is associated with the percolation threshold itself, which grows exponentially. The second regime displays an algebraic growth with an exponent of 1/3 and we argue that it must be associated with the direc- tional connectivity of the wetting phase to the substrate.