First, a shout out to masonsailor2 for inspiring me to attempt a salt and pepper mill (https://forum.shopsmith.com/viewtopic.php?p=258147#p258147) for the first time. I am still new at woodturning, so these salt & pepper mills (see below) are far from perfect, but I was attempting to copy the design of a salt & pepper mill set that I bought previously. So, here is my question. For woodturning, should I expect concentricity between a drive hub and a chuck? I followed a video online for how to turn salt & pepper mills. I started with a single blank between my Shopsmith drive hub and a live center in the tailstock. I rounded this blank, then cut tenons on each end for chucking the blank. Next, the blank is drilled for the salt/pepper cavity inside. Then I cut the tenon in the salt/pepper mill top, then parted the top from the bottom of the blank. From this point on, you are supposed to switch to using a lathe chuck to drive the blank which is what I did. This is where I encountered the problem. I had to re-turn the blank for roundness when switching from the drive hub to the lathe chuck. Why is this? I would have expected the center of the drive hub to match the center of the lathe chuck, but this was far from the case. I should point out that I did align the drive hub to the tailstock live center and confirmed this multiple times. Also, I am using the Nova G3 chuck with the Shopsmith arbor adapter and the chuck is assembled correctly, i.e. the numbered jaws match the chuck numbering.
I know there are different techniques to go about a particular task in woodturning like this one. Just wondering what I did wrong, or whether this is a common thing known in woodturning, i.e. that you can't go from a drive hub to a chuck turning without having to start over due to the lack of concentricity.

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