The graphite is not always well centered in the pencil, but sharpening it and then rotating it inside your jig should always resolve that by either drawing a dot in the best case or a small circle in the worst. Plus, it’s easy to tell visually if the graphite is well centered by looking at whether it’s border with the wood is elliptical or circular.
You probably already figured this out but at the risk of stating the obvious in case it helps, the Google recommendation was for finding the brand so you can find compatible better soldering iron tips.