Currently, when a quest is completed, players are able to join your lobby and start the game, while players are still in at the end of the quest. Usually when new players join, they immediately start the quest and force the other players who just completed the quest, into their new game.
I propose that the lobby remain locked while there are still active players at the end of the quest. Most of the time when I complete a quest, one or two people hang around to chat, send friend requests, plan another activity, and generally have a few moments of celebration. It's also unlikely that players who just completed the quest will want to be part of the new game. And since the newly joined players are in a different are of the quest, they can't hear the voice chat and usually don't know that they joined a group that just finished.