Photovoltaic devices based on Cu(In,Ga)Se2 (CIGSe) absorbers are among the most attractive non-Si alternatives. The key to their steadily increasing efficiency is a post-deposition treatment (PDT) with alkali salts. For coevaporated CIGSe, a RbF-PDT was demonstrated as the most efficient, however, the mechanism of the RbF influence on the CIGSe absorber is not completely understood. Here, we focus on the impact of RbF on the surface of co-evaporated CIGSe absorbers in dependence on their bulk composition. Surface-as well as bulk-sensitive methods with overlapping information depths are used to examine an overall depth profile of RbF-free and RbF-treated CIGSe samples with different Cu contents. We show a gradual depletion of copper towards the surface for the as-deposited CIGSe absorber layers. The following RbF-PDT sharpens this effect especially for the sample grown with the overall lower Cu content. Under the Cu-depleted surface layer, the composition of the CIGSe gradually changes until it reaches the respective bulk composition. As a result of the RbF-PDT, Ga diffuses towards the surface and Rb gets incorporated at the surface where GaF3 and RbInSe2 secondary phases are formed, respectively. A higher Cu content leads to less surface oriented Ga diffusion, less Rb incorporation and to a thinner RbInSe2 layer. A thinner RbInSe2 barrier layer, in turn, maintains the gain in open-circuit voltage and prevents the fill factor loss of the CIGSe device.