I have been warned about crossing behind and below the A380 a few times in European airspace.
I have been vectored in order to get further away from it, and I have been asked to climb 1000 ft to get above the wake. We were to heavy but the controller was happy to let us climb two hundred feet and then return to our cleared altitude after we passed the A380 track.
Not sure if the controllers have to do any active separation, but I don’t mind if they do. I fly 737.