We present a theoretical density-functional theory study on the deposition of metal atoms (Ir, Pd, Pt, Ag, and Au) on FeO(111) and MgO(111) monolayers supported on Pt(111). We show the existence of a strong coupling between the charge state of the adsorbed adatom and the local polaroniclike distortion of the oxide film, and we identify two qualitatively different adsorption modes in which the distortion either reinforces the rumpling of the supported oxide film (positively charged adsorbates) or reduces or even reverses the cation-anion stacking (negatively charged adsorbates). Thus, the adsorption mode is a response to the charge state of the adsorbate and is driven mainly by the capacity of adatoms to exchange electrons with the support.