I don't follow the Rays day in and day out so I might be missing things, but I've never gotten the impression that Madden is some kind of extraordinary manager. He has received a lot of support from sabermetrically inclined writers and analysts, but I have yet to read a convincing, detailed statistical account as to what exactly he does that separates him from the rest of the managers in baseball. I feel like he gets the benefit of the doubt since he had worked with THE sabermetric front-office for so many years, and if they stick with him then he must be good.
Undoubtedly, there are things he does well. I think he has been very good at maximizing his roster by using platoons and positioning to put his players in the best position to succeed. Additionally, he seems to be able to foster a great clubhouse culture. However, in other ways he is still fairly standard. His intentional walk numbers are league average, as are his sacrifice bunt numbers. Also, I haven't notice that his bullpen usage is particularly unconventional.
I am definitely open to having my mind changed if others have strong arguments in Madden's favor. But considering that it sounds like he wants to be one of the top-paid managers in the game, I'm not sure he is worth it.