Based on an accurate determination of the potential energy surfaces of Rb3+ correlated to its first asymptotic limit Rb++Rb(5s)+Rb(5s), we identify the presence of intersections of a pair of singlet and triplet surfaces over all interparticle distances, leading to Jahn-Teller (JT) couplings. We elaborate scenarios for charge exchange between ultracold charged atom-dimer complex (Rb+Rb2+ or Rb++Rb2), predicting a strong selectivity on the preparation of the initial state of the dimer. We also demonstrate that the JT couplings must drive the three-body recombination (TBR) of Rb+, Rb, and Rb at ultracold energies. Using the current analysis, we provide a consistent picture of the TBR experiments performed in ion-atom hybrid Rb samples. We also demonstrate the presence of JT coupling as a general phenomenon in the singly charged homonuclear alkali triatomic systems. Published by the American Physical Society 2024