Yah the advantage of a proxy war is that someone else gets to be called genocidal.
The situation of the Kurds is different though. The Kurdish in adjoining states are kept stateless by intent of those other states, regardless of whether that intent gets expressed in cooperative ventures, which is not necessarily or even usually the case.
In Ukraine, however, Russia wants to reclaim the 'separatist' turf in eastern Ukraine, as well as accommodate the Russophiles who live there. It's true that in the conflict in Ukraine in 2014, the Rostov area of Russia saw an influx of refugees from the Ukraine border area. But this time around the Russians have actually prepared that area for immigration and are now urging civilians to evacuate the Donbas area of Ukraine before 'bad things happen'.
Of course Putin also proposes that the 'bad things' will be the doing of Western supporters of Ukraine... even though it was Russian-backed separatists and not the West that shelled a kindergarten and a number of other facilities in eastern Ukraine per numerous reports from the OSCE in recent days. Putin's dodge on that is another example of slice-and-dice proxy wars. Sometimes he embraces the separatists, other times it's more convenient to say hey that wasn't us...