It is generally accepted that relativistic jet outflows power the nonthermal emission from active galactic nuclei (AGN). The composition of these jets - leptonic versus hadronic - is still under debate. We investigate the microphysical details of the conversion process of the kinetic energy in collimated relativistic pair outflows into radiation through interactions with the ambient interstellar medium. Viewed from the coordinate system comoving with the pair outflow, the interstellar protons and electrons represent a proton-electron beam propagating with relativistic speed in the pair plasma. We demonstrate that the beam excites both electrostatic and low-frequency magnetohydrodynamic Alfven-type waves via a two-stream instability in the pair background plasma, and we calculate the time evolution of the distribution functions of the beam particles and the generated plasma wave turbulence power spectra. For standard AGN jet outflow and environment parameters we show that the initial beam distributions of interstellar protons and electrons quickly relax to plateau-distributions in parallel momentum, transferring thereby one-half of the initial energy density of the beam particles to electric field fluctuations of the generated electrostatic turbulence. On considerably longer time scales, the plateaued interstellar electrons and protons will isotropise by their self-generated transverse turbulence and thus be picked-up in the outflow pair plasma. These longer time scales are also characteristic for the development of transverse hydromagnetic turbulence from the plateaued electrons and protons. This hydromagnetic turbulence upstream and downstream is crucial for diffusive shock acceleration to operate at external or internal shocks associated with pair outflows.