What happened with Oki can happen with any manager.
You have a guy who's usually effective. He is crap today. You have two choices, and you have them with every plate appearance.
1: Sit there and wait
2: Pull him and bring in another pitcher.
Neither of these is an excellent choice. You're either burning an additional pitcher, which can bite you in future games, or you're trusting a guy who isn't good today, which can burn you now. How you manage that decision and the kind of heat you can take if it goes wrong is why Tito gets paid as much as he does.
Remember, Hideki Okajima is a good relief pitcher. Regardless of how you feel about him at the moment over the course of a season he's consistently one of our best. Oki letting in some hits, maybe even a run, then bouncing back and putting up those three outs himself was a distinct possibility even at the time he actually did get him. It is not as cut and dried as simply "well he's let on some baserunners, time to go get him." That adds strain to your bullpen and should be avoided if possible if you want to make it to September with 12 healthy arms.
So with a big lead in hand he pushed his veteran a bit trying to squeeze an out or two out of him. Any manager does that if he has the leeway in a given game to get away with it. Pulling him before the first run scored would have been a panic move with a 6 run lead.
Personally I think that Oki could have come out a couple bats earlier, and Tito wanted to give him a chance to bounce back -- but he hedged his bets by warming up Papelbon instead of Bard so that if things really went to hell -- like they did -- Tito could roll his best reliever out there rather than trust Bard, Delcarmen and RR, all of which have just as many warts as Oki.
I just don't see too many managers who would have run that inning differently given the same parameters.