the tailstock is almost never exactly on center. I suggest a dial indicator and the roundest piece you've got, perhaps a large endmill in the chuck. Forget the tailstock, chuck it up, put the dial indicator on it,and see where it is off and tap the chuck to center. Most 3-jaw will runout about .003. You may be able to get it closer, but repeatability will always be an issue, especially with a threaded chuck.
when I had a lathe with threaded spindle, I'd spin it on to hand tight, then back it off, spin it back on about three times to seat it. Clean (!) threads will help a bunch.
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