MoS2 and other transition metal dichalcogenides are considered as potential materials in many applications including future electronics. A prerequisite for these applications is to understand the nature of the MoS2 contact with different metals. We use semi-local density functional theory in conjunction with dispersion corrections to study the heterostructures composed of Pd and Pt monolayers with (111) orientation grown pseudomorphically on MoS2(001). The interface properties are mapped as a function of the number of deposited overlayers, as well as a function of tensile and compressive strains. Although we show that the dependence of the contacts on strain can be fully explained using the d-band model, we find that their evolution with the number of deposited metal layers is markedly different between Pd and Pt, and at variance with the d-band model. Specifically, the Pt/MoS2 heterostructures show an anomalous large stability with the deposition of two metal monolayers for all investigated strains, while Pd/MoS2 exhibits a similar behavior only for compressive strains. It is shown that the results can be rationalized by accounting for second-nearest-neighbor effect that couples MoS2 with the subsurface metal layers. The underpinnings of this behavior are attributed to the larger polarizability and cohesive energy of Pt compared to Pd, that leads to a larger charge-response in the subsurface layers.