Recent studies on graphene hydrogenation processes showed that hydrogenation occurs via island growing domains, however how the substrate can affect the hydrogenation dynamics and/or pattern formation has not been yet properly investigated. In this work we have addressed these issues through fully atomistic reactive molecular dynamics simulations. We investigated the structural and dynamical aspects of the hydrogenation of graphene membranes (one-side hydrogenation, the so called graphone structure) on different substrates (graphene, few-layers graphene, graphite and platinum). Our results also show that the observed hydrogenation rates are very sensitive to the substrate type. For all investigated cases, the largest fraction of hydrogenated carbon atoms was for platinum substrates. Our results also show that a significant number of randomly distributed H clusters are formed during the early stages of the hydrogenation process, regardless of the type of substrate. These results suggest that, similarly to graphane formation, large perfect graphone-like domains are unlikely to be formed. These findings are especially important since experiments have showed that cluster formation influences the electronic transport properties in hydrogenated graphene.