Present-day structural and kinematical properties of multiple populations (MPs) can provide useful information about the physical mechanisms driving the formation and early evolution of globular clusters (GCs). As part of a large project aimed at characterizing the kinematics of MPs, here we present a detailed multi-epoch analysis of the low-mass GC NGC6362. We find that MPs in this system show significant differences in their line-of-sight velocity dispersion profiles. This result is totally unexpected given the dynamical age and fraction of mass lost by NGC6362. We also find that the binary fraction is remarkably larger in the first (FP) than in the second population (SP). We show that such a difference can efficiently inflate the velocity dispersion of FP at intermediate/large cluster-centric distances with respect to SP. Indeed, our results nicely match the predictions of state-of-the art N-body simulations of the co-evolution of MPs in GCs including the effect of binaries.