The instructions you have with your pattern make good sense. Knitting 19 and then 2 tog turns out with one stitch left on the end that is knit. Since you have to seam your hat up that stitch will be eaten up in the seam so it should come out perfectly with 19 stitches between the decreases all around. The other rows will turn out the same way with an edge stitch, but when you seam it everything will be even.
What KnitQueen said will work too, but knitting 19 will produce 4 decreases in a row and knitting 15 will end up with 5 decreases in a row, so the top of the hat will pull in faster than your pattern calls for, not that that won't work, it will, but it will be different than the one you are looking at in your pattern. Also 15 fits into 85 with the last K2tog right at the end of the row, so you don't have a seam stitch, so that one segment will be one stitch smaller than the others. This is not to lose sleep over though, and will probably not be noticed. I just mean to point out that the pattern is well written and makes good sense.
You asked about why you don't decrease on every row. You can if you like, but the designer didn't do his/hers that way. With hats you can do just about anything you want and get a hat of some sort, some better than others. I've seen hats that decrease all in one row, or don't decrease at all, anything is possible. That is why hats are such fun to do and to just make up as you go along. But if you desire a hat to turn out like one pictured with a pattern it is probably best to do what they did, at least until you gain enough experience to know what will happen if you don't, or how to get their result an alternate way.