Yes, there are button bands. The pattern calls for 10 buttons so they are in the back. You make the top from side to side with a back opening, pick up stitches and add the dark band at the top and then knit the two button bands and sew them on. It says in the finishing to "attach" the bands. That would be sewing.
You are right about no beginning * and the directions for the button band are weird to me. They are:
Left Button Band:
CO 12 sts. Work entire band in single rib.
Work 4 rows. Work 2-row buttonhole.
(Note: Each buttonhole is worked over 2 rows.)
Work 6 rows. Make Buttonhole.
Work 8 rows. Make Buttonhole.
Work 14 (15, 16) rows. Make Buttonhole. Repeat from * 7 more times. Work 4 more rows, then BO all sts in rib.
You need to make 10 buttonholes according to the number of buttons it says you need for the project. I don't know why you would want to space the button holes 4 rows, 6 rows, 8 rows, 14 rows apart. I don't know where the * would be to repeat it 7 more times for 10 buttons. Here is a case of "you don't have to do what they say". If you want a sewn on button hole band you can do like they say about the cast on, but I'd try to space the buttonholes evenly.
If it was me, I would opt to pick up stitches on each back for the band, and add the buttonholes on the one side.