There's no real way for us to know that. Cairne died between WotLK and Cata, some time ago, and we don't really know when the "machinery of Death" broke down and started consigning souls to the Maw by default. We know it was broken as of the Battle of Thorns and the burning of Teldrassil, but not exactly when before that. There's also many, many ways in which souls could avoid consignment to the Shadowlands (and thus the Maw) entirely. We see evidence of that with souls drawn to Bwonsamdi's temple complex post-Teldrassil (when we know Death itself was broken), with ghosts and specters of the Drust, and so on. The Maw is not an absolute destination and it's just that now if you aren't somehow bound to the physical world as a ghost, or snapped up by another power like Bwonsamdi or Odyn, you go to the Shadowlands and thus the Maw.