In my book, Hummingfrog is right in what he says, but that is not quite the whole story. The helicopter is controlled and manipulated by the pilot, who uses visual cues to decide what to do and when.
As Crab suggests, a downwind demo of VRS will be likely to involve starting at a negative speed hover wrt the air (or at least a lower airspeed than into wind). There seems to me to be 2 possibilities:
The recovery is standard (i.e. does not vary depending upon the relative wind).
In this case, a "standard" amount of nose down will initiate the recovery. But with downwind the pilot will wait longer to see the positive (30+ kts) IAS that he requires before doing the rest of the recovery. Because he waits longer while descending, the aircraft will descend further.
The recovery is varied to take account of relative wind
Knowing that he is downwind with lower/negative air speed the pilot chooses a larger nose down attitude when downwind. That has the same net effect that the total descent will be greater than for into wind, before positive IAS is achieved.