Rarely would I consider using a drill to help one take a divot after contact, rather than before. Why? Because there is a reason one would hit behind the ball, and you should focus on correcting that, not putting a Band-Aid on it.
Three primary reasons for fat shots come to mind.
1) Faulty balance/swing center control.
2) Faulty set up.
3) Poor transition from the loading motion to the downswing.
If those are not correct, all the divot drills in the world won’t help your game. You’ll just hit different bad shots.