There is very little evidence in NFL history that defenses coaches that "chase" turnovers succeed with any real success. And this all comes from Monte Kiffin (who was the real mastermind behind the defense and who Tomlin worked under from 2001-2005.
Here is an excerpt of his wikipedia page:
https://en.wikipedia.org/wiki/Monte_Kiffin
Monte Kiffin is the mastermind behind the Tampa 2 scheme, which is a slight modification of Tony Dungy's Cover 2. His defensive philosophy has several hallmarks.
1. Speed over size and strength. Coordinators that employ Kiffin-style defenses will often replace linebackers with safeties in order to put more speed on the field. In particular, linebackers must be able to cover receivers; in the Tampa 2 scheme, one linebacker frequently drops back deep into coverage, turning what looks like a Cover 2 defense into a Cover 3. Kiffin's defenses also employ quick, penetrating defensive tackles.
2. Preventing scores over preventing yardage. A Kiffin coordinator doesn't care how many yards an offense gains, as long as the team doesn't score, an approach known as bend-but-don't-break.
3. Multiple defenses from one look. Kiffin-style defenses try to use the same personnel (or the same kind of personnel) at all times, so that the offense cannot adjust its play call based on the alignment of the defensive personnel.
4. Attacking and causing turnovers. Kiffin-style defenses focus on getting the ball away from the offense by stripping the ball away from the ball carrier or reading the quarterback to make an interception. The risk is that if the ball is not stripped or intercepted, then the ball carrier on offense has a better chance of gaining more yards or scoring; the reward is that the offensive drive is stopped without a score more often, frequently giving good field position.
Starting to sound familiar? Stuff we start hearing about now that Lebeau is out the door? All the blips and quotes from camp leaning this way?
It basically comes down to whether you like the Dungy/Kiffin coaching tree or not (on a defensive side of the ball) and I am emphatically not a fan. This defensive tree is as follows: Lovie Smith, Herm Edwards, Mike Tomlin, Leslie Frazier and Rod Marinelli.
ALL of those supposed defensive gurus chased turnovers often at the expense of yards and points.
And when turnovers failed to happen, their defenses suffered. And turnovers are hard to coach or depend on. You look through their coaching records and turnovers bounce from 3rd one year to 20th the next. And whole seasons were lost by these coaches because of the lack of turnovers and the defense has no way to stop an offense any other way.
It's a stupid system and I'm scare to **** this is the way we're headed. You'll have great years. It happens. And you guys might think I'm stupid if we get a rash of turnovers this year and point at how wrong I am. But historically, turnovers don't last. Not nearly as year-in, year-out as a PHYSICALLY big, attacking, sack-oriented defense does. For the most part sacks do stay constant and are more dependable to your personnel.