The center finder is for marking the center. Even if you're using the other jigs and ideas, its not a bad idea to have a clear indication of where the center is anyway. That said, even 1/8" dowels can use this method fine, I do it all the time (I do inlayed "dowels" for fretboard markers frequently, it requires absolute precision).
Using the awl provides accurate referencing for the drill bit, and works EVERY time on any size dowel. If your stock isnt lined up or your drilling technique is off, then yeah you might have issues with drilling through the sides. Im not even sure how you even could mess up my technique tbh, its foolproof and doesnt waste time with jigs and fiddling with complicated table setups. If you're drilling by "hand", I assume you mean a cordless drill running it through? That'd be difficult to do with almost any setup and would require a lot of practice.