And they all rapidly matured the second the trade happened.
That sounds like quite the miracle coincidence.
Nope. You seem to be ignoring the fact that the team was already very good for a while before Perkins even played a game, as evidenced by their 92-55 record in the season and three quarters prior to his debut.
More specifically, they had 50 wins the prior season, and were on track for 52 wins prior to getting Perkins (and finished with 55). Then they were on track for 58 wins in the lockout season, and are likely to win 60+ this year.
So yeah, maybe adding Perkins got resulted in a couple of extra wins each season. But nothing "miraculously" happened the minute they made the trade. The evidence for gradual improvement, likely due to their best players coming into their own, much stronger.