My first thought when I saw the pic was standard bushings gouging the center. Don't ask how I know. I'm using the same live center you just bought from PSI and it works fine with the right bushings (or even with none) I do still sometimes use a mandrel to get the blanks rounded off so it doesn't catch and spin the bushings on the centers. It avoids extra wear and tear (read: expense).
As Sam
@Dehn0045 said, a 7mm set works to get you most of the way done. These
7mm adapter bushings are top notch and fit right into the standard bushings. Though I don't see him much on the forums, the owner/machinist is a member here. You can always add more specific TBC bushings down the road.
I have a ways to go before I'm as skilled as many pen makers here, but this is what works for me so far. I turn them down almost to the bushings, then set the tube directly on the centers to finish them, using calipers to measure, and very gentle pressure from the tailstock. Since the final cuts are essentially just a light shaving, the tubes shouldn't catch and spin on the centers. I wax the centers before putting tube on directly so I can just apply the CA finish while it's on there without as much trouble cleaning the centers when I'm done.