I have imported a dataset full of names and centered the bound object on the page to the center of the artboard. However the other instances of the datasets are not positioned in the center, the further through the dataset it seems to have absolutely no central point at all?
Draw and design
I believe the extra long lines of this font which somehow overlap the standard character space that our text defaults with causes the bounding box to shift. In fact, the center-justified anchor does hang around in the same spot - it's the boundaries that move.
Maybe you can try to mess with the optical alignment in Type menu item at the top of the app. When I changed it, my box moved a little bit. Even if there is something strange with the font or something that is making this do a little shift outside of your control, maybe you could brute-force it by using actions to always center this textbox. This would have to become part of your batch export process, and you can even test this live by recording an action which first cycles the dataset to next and then does the alignment (I call this post-processing).
However even so, the results may not be what you may want in the end. The fact is, this font differs from a more standard font and it affects the character positioning with all the various styles going on. With potentially a very skinny character having a high visual weight or vice-versa, a very large character in width whose art is actually very small or spread-out, these alignments are more into the realm of arbitrary. There are a lot of character combinations which would need a special form of handling to be aligned 'center' in just the way you want. In fact, this font appears to be taking an opinionated and crafted approach to this in your problematic case.
This G has a tail that pushes the box to the left, but that part of the character is just for show so it cuts off the text baseline at where the G body starts. But it moves the bounding box, because, technically that part is still a physical constituent of that art. So if you actually used actions or something to move the box and align it to the center of the artboard, it may shift the design in a bad way. Maybe the way it's acting is producing the better visual result.