This is one of the things that isn't spelled out well.
"During his or her turn, each player should take a flea token from the supply and place it—active side face up—on a tile which is adjacent (horizontal or vertical, not diagonal) to the Outbreak, and which does not yet have a flea on it. As play continues, one may alternatively place a flea on a tile adjacent to one with an active flea"
The "one may alternatively" line makes me believe that after the first flea is placed next to the plague tile, the next player can grow the plague from the flea and leave the plague Outbreak tile empty on one side. We have only played this once and in every case, the plague tile was placed where it was only touching one tile, so we didn't have to worry about it.