If I use Captivating Poke Puff and put one of my opponent's Basic Pokemon on the bench that has an Ability (like Shaymin EX's "Setup"), does the opponent get to use that Ability right away?
No, Captivating Poke Puff does not trigger any coming into play Abilities.
Source: Steam Siege FAQ (2016-08-04), TPCi Rules Team (2016-08-04)

Relevant cards

Note: All applicable cards may not be listed below.
XY11_99