I'm going to go back to Tito here for a couple of points:
Tito understands the psychology of pitchers. First, Tito usually would pull a pitcher before REAL trouble gets rolling. He'll pull a guy who's struggling regardless of the number of pitches thrown. During his tenure in Boston it was obvious to me that his goal was to protect his starters, to make them feel they'd been successful when they come off the mound because Tito knows that if you feel like you're successful you'll have a better chance of actually being successful in your next outing.
Tito also learned at the Bill James school of Relievers. James has always said that the time to use your best pitcher may not be in the 9th inning. It's when you can bring him in to avoid a big inning. That's what Tito's been doing with Miller. Use your best pitcher to keep you from getting behind. Pretty simple stuff.
And in a related thought.....I've often wondered about the wisdom of saving your best reliever for the 9th inning. Doesn't that imply that the batters coming up in the 9th 'turn it up a notch', and that they'll hit better in the 9th than any other time in the game? If you've got a shut-down guy don't save him for the 9th, use him to shut down regardless of the inning. As Ralph Houk said, "Don't save a pitcher for tomorrow. It may rain tomorrow." Don't save a pitcher for the 9th. You may not need him for the 9th, especially if you've let your team get behind earlier in the game.