Scoring extra points for winning
A winning bonus are points that go to the winner and the winner only. In some versions of mahjong all players gain points, meaning that the winning bonus is an encouragement to go out quickly if you have a bad hand. In the old Hong Kong version, there is no bonus while in Korean rules the bonus, depending on the version, can be very generous (upto 5 points extra just for winning, doubled if completely concealed.
Winning bonus and doubling
In versions where points are doubled based on what kind of hand one has, the winning bonus is usually included before the points are doubled. In all cases where payment is doubled being east, winner, discarding the winning tile, the winning bonus is included before doubling.
Variations and the utility of winning bonuses
Based on how casual players are with each other, the winning bonus (as with all scoring between players familiar with each other) can be modified depending on how they see the game. If the challenge of making a complex winning hand is more important for a group, they may consider lowering the bonus and giving higher points for complex hands. However, if having a fast game is more important, than the bonus is a good incentive to keep the fast quick and enjoyable.