According to my book, the pleats are not sewn from inside, but from the outside.

Start at the bottom and work toward the waist.

I'll see if I can explain the stitch. Since I've learned it, I use it on a lot of things where I want a nice, tight seam.

Start with the fabric on the bottom layer of fabric. Catch a few threads, bring the needle straight up and catch a few threads on the edge of the fold. When you pull tight, the two layers of fabric should snug up together. Catch a few threads from the bottom layer, bring the needle up and catch a few threads on the edge of the fold, and pull snug once again. Since you're pulling the two layers of fabric together, you can use the stripes on the tartan to keep things straight. Hope this helps. I also tried to draw a diagram.

<waist --- bottom>
x x x x x x x x x x x (folded edge on top layer of fabric)
|/|/|/|/|/|/|/|/|/|/| (Thread direction)
x x x x x x x x x x x (bottom layer of fabric)