The way Shaymin reads is: "When *you* play this Pokemon from *your* hand onto your bench,..."
Lele: "When *you* play this Pokemon from *your* hand onto *your* bench during your turn,..."
Most other cards with abilities that trigger on playing have similar wording, or at least include the word(s) "you" or "your" in the ability text. When Puff is used, it is used by your opponent and "you" are not playing the card from your hand to your bench, it is getting pulled from your hand by an external effect. From the playing party perspective, it would be going onto your opponent's bench, not yours, therefore you would not get the benefit of any ability. The only benefit you derive is preventing your opponent from utilizing the ability.