I had some templates made for my watch straps and I still have to work to get my holes lined up straight. However, in my experience, it's a combination of things that contributed to the holes being misaligned.
As others have mentioned, I mark the holes with a nail, then I use my scratch awl to make a proper indentation. Then I use the hole punch itself and press it into the leather just enough to leave a mark. I measure the mark and ensure that it's straight, then punch.
However, I found that punching my holes with the strap faced perpendicular away from my body helped me align things better. When I had it facing parallel with my chest, my holes were almost invariably crooked. Since changing position, they have improved remarkably. I also have seen a great improvement by punching on a marble slab with my self-healing cutting mat on top of it. With this method, I was able to get these holes: