The fate of dimethyl ether (DME, CH3OCH3) in collisions with He+ ions is of high relevance for astrochemical models aimed at reproducing the abundances of complex organic molecules in the interstellar medium. Here we report an investigation on the reaction of He+ ions with DME carried out using a Guided Ion Beam Mass Spectrometer (GIB-MS), which allows the measurement of reactive cross-sections and branching ratios (BRs) as a function of the collision energy. We obtain insights into the dissociative charge (electron) exchange mechanism by investigating the nature of the non-adiabatic transitions between the relevant potential energy surfaces (PESs) in an improved Landau-Zener approach. We find that the large interaction anisotropy could induce a pronounced orientation of the polar DME molecule in the electric field generated by He+ so that at short distances the collision complex is confined within pendular states, a particular case of bending motion, which gives rise to intriguing stereodynamic effects. The positions of the intermolecular potential energy curve crossings indicate that He+ captures an electron from an inner valence orbital of DME, thus causing its dissociation. In addition to the crossing positions, the symmetry of the electron density distribution of the involved DME orbitals turns out to be a further major point affecting the probability of electron transfer. Thus, the anisotropy of the intermolecular interaction and the electron densities of the orbitals involved in the reaction are the key "ingredients" for describing the dynamics of this dissociative charge transfer.