Your holes can be dead nuts center, and threads cut dead nuts center to the holes, and still get .0025" runout on the pin, especially if you are bottoming out the pin. There's at least that much slop in the grooves of the threads. You can avoid it by using flat minor style threads, or else grind the threads instead of tapping and cut them to match the OD of the pin, to avoid settling to one side or the other. Otherwise, just a v-groove pin & tapped hole is not good enough for accuracy. Never has been & was never meant to be. This is why in mechanical situations where bolted together parts require accurate alignment, there is a pilot.
In short, it seems to me your tap is cutting threads deeper than your pin's threads, giving room for slop. It's tough to describe but very simple stuff & often overlooked. VERY common problem. Point being, if you want your shaft to fit flush to the butt, then you need to be sure your joint has a way of aligning the two parts to come together on center. A standard 3/8-10 with tapped holes simply doesn't offer that.
I Build the butts of my cues & have them prepped for finish before I even choose shafts for it. I make the shafts & then shave them down to the matching diameter of the butt. They always fit flush. Often, the shafts never get screwed onto the butt until the cue is finished & ready to ship. It's because my joint system is so repeatable & accurate. I use a flat minor pin that has a .3115" minor and it fits a hole that gets reamed to .312". It fits too tight to screw together so I have to coat the internal threads of the shaft with a lube. Then it fits smooth and feels snug but right as you are putting the cue together. I have my pins made to match my tooling exactly, and finish arbors to match my pins exactly. I struggled with the same issue you are having for a while. It sucks. But it's not necessarily you or the machine screwing it up. It's the nature of v-groove threads cut with a tap. To be honest, the fix will cost you quite a bit. Or you could try using Radial pins & tap and follow the directions exact. That'll get you a really good fit without costing much.
Otherwise you can accept the slop of your fit and roll with it. Screw the shaft on snug and chuck up the assembled cue, then shave/sand the joint area until the shaft & butt are concentric. Seems to be what a lot of folks do but it's just putting lipstick on a pig. Much better if everything fits right every time, every step of the way. Feels better, too, knowing it's right. Truth is that the difference likely doesn't affect playability, but if you take short cuts here then where else do you take short cuts? Multiple short cuts in a cue will certainly have the potential to affect playability, and longevity.