I think the right shoulder and the axis tilt basically plays the same role on EP as on TSP even though the geometry is slightly different.
You basically bring the arms back to a place where everything is well connected (whether you're a TSP-er or an EP-er). From there, the EP-er goes deeper with the right shoulder due to more increase in lateral bend of the spine. No independent arms motion until later in the down swing - much later than if you swing on the TSP and throw the right arm off the chest during transition.