Atoms and molecules attached to rare-gas clusters are ionized by an interatomic autoionization process traditionally termed "Penning ionization" when the host cluster is resonantly excited. Here we analyze this process in the light of the interatomic Coulombic decay (ICD) mechanism, which usually contains a contribution from charge exchange at a short interatomic distance and one from virtual photon transfer at a large interatomic distance. For helium (He) nanodroplets doped with alkali metal atoms (Li, Rb), we show that long-range and short-range contributions to the interatomic autoionization can be clearly distinguished by detecting electrons and ions in coincidence. Surprisingly, ab initio calculations show that even for alkali metal atoms floating in dimples at a large distance from the nanodroplet surface, autoionization is largely dominated by charge-exchange ICD. Furthermore, the measured electron spectra manifest the ultrafast internal relaxation of the droplet mainly into the 1s2s1S state and partially into the metastable 1s2s3S state.