The basic properties of the candidate binary cluster population in the Magellanic Clouds and Galaxy are similar. The fraction of candidate binary systems is $sim$10% and the pair separation histogram exhibits a bimodal distribution commonly attributed to their transient nature. However, if primordial pairs cannot survive for long as recognizable bound systems, how are they ending up? Here, we use simulations to confirm that merging, extreme tidal distortion and ionization are possible depending on the initial orbital elements and mass ratio of the pair. The nature of the dominant evolutionary path largely depends on the strength of the local tidal field. Merging is observed for initially close primordial binary clusters but also for wider pairs in nearly parabolic orbits. Its characteristic timescale depends on the initial orbital semi-major axis, eccentricity, and cluster pair mass ratio, becoming shorter for closer, more eccentric equal mass pairs. Shredding or extreme tidal distortion of the less massive cluster and subsequent separation is observed in all pairs with appreciably different masses. Wide pairs steadily evolve into the separated twins state characterized by the presence of tidal bridges and separations of 200-500 pc after one Galactic orbit. In the Galaxy, the vast majority of observed binary candidates appear to be following this evolutionary path which translates into the dominant peak (25-30 pc) in the pair separation distribution. The secondary peak at smaller separations (10-15 pc) can be explained as due to close pairs in almost circular orbits and/or undergoing merging. Merged clusters exhibit both peculiar radial density and velocity dispersion profiles shaped by synchronization and gravogyro instabilities. Both simulations and observations show that, for the range of parameters studied here, long term binary cluster stability in the Galactic disk is unlikely.