"All moves or abilities that would normally increase a stat will decrease it, and ones that would normally decrease a stat will increase it. This also applies to self-inflicted moves, such as Charge Beam, Close Combat and Leaf Storm. "
"Psych Up copies both the positive and negative changes to the target's stats and replicates them onto the user. The target's Attack, Defense, Special Attack, Special Defense, Speed, Accuracy and Evasion are copied. Any changes made to the target's stats after Psych Up is used will not affect the user's stats. "
Psych up only COPIES the stats directly, whereas the stat dropping moves, like overheat, already have a preset effect on the stats, since they are already set to lower stats, they are reversed, and would otherwise raise stats. I could be wrong, and am only going based on the descriptions. This if a good thing for Will to test out.
http://bulbapedia.bulbagarden.net/wiki/Antagonist_(ability)