We investigate the phase coupling between spatially separated polariton condensates under nonresonant optical pulsed excitation. In the simple case of two condensates, we observe phase locking either in symmetric or antisymmetric states. We demonstrate that the coupling symmetry depends both on the separation distance and outflow velocity from the condensates. We interpret the observations through stimulated relaxation of polaritons to the phase configuration with the highest occupation. We derive an analytic criterion for the phase locking of a pair-polariton condensate and extend it to polariton multiplets. In the case of three condensates, we predict theoretically and observe experimentally either in-phase locking or the appearance of phase winding with phase differences of �2π/3 between neighbors. The latter state corresponds to a vortex of winding number �1 across the three polariton condensates.