We present a combined ion imaging and density functional theory study of the dynamics of the desorption process of rubidium and cesium atoms off the surface of helium nanodroplets upon excitation of the perturbed 6s and 7s states, respectively. Both experimental and theoretical results are well represented by the pseudodiatomic model for effective masses of the helium droplet in the desorption reaction of m(eff)/m(He) approximate to 10 (Rb) and 13 (Cs). Deviations from this model are found for Rb excited to the 6p state. Photoelectron spectra indicate that the dopant-droplet interaction induces relaxation into low-lying electronic states of the desorbed atoms in the course of the ejection process.