I've watched some OK St games on YouTube and very much enjoy watching their offense. Tons of cutting and dribble handoffs. Not much standing around. I don't necessarily see a natural fit with a posting big man like Tilmon, but I haven't seen much of his game. I'm sure Underwood would have a carve out a clear role for him.
In the halfcourt Tilmon would have multiple opportunities to do what he does. He will be able to score on a pick/handoff and roll, probably 2-3 times per possession. If he's not hit on the roll, he will be told to immediately post, where the ball handler will be taught to look for him again. If he's not open on the roll post, the ball will be reversed one pass to a guy filling the slot. Tilmon will be taught to repost for a high-low look on a pass from the slot. If he's not open then the ball will be reversed and the continuity started again.
If he's on the perimeter for whatever reason, he would be a great second cutter because that guy gets a screen into a post up iso.
Others who have seen Tilmon play more can speak to his high post game better than me, but if he can face up at the elbow and hit an elbow j, or pump fake/jab/sikma step and score from there off one dribble, he will be very hard to guard in this offense. That's the only layer of his game I'm unsure of, I don't know how comfortable he is in the high post and putting the ball on the floor. But it's hard to double the elbow based on the spacing of the offense, so he's gonna have room to work if he's comfortable there.