It's a while since I've done this but as far as I remember, for the circular piece the process is the same as centering in a four jaw chuck - treating the rotating table as a chuck. I suppose it depends on your clamping mechanism as to how easy this is. A hinged DTI holder so you can lift the DTI out of the way and then drop it back in precisely the same position helps.

Another method is to turn a plug to go into the central hole of the table which then locates in in a hole bored in the workpiece but it's not always possible to do this and you need to get a good fit for accuracy.

If you can mark the centre of rotation on the workpiece with at least a good centre punch, you could use a dead centre between the point in the punch hole and and another centre or similar in the mill chuck and put the DTI on that.

Good luck,
Mark