It depends on the look of the pattern. Does the pattern say to knit 8 rows of stockinette or does it just say to knit 8 rows? You don't HAVE TO purl the wrong side of every garment you do. If you did that you'd end up with nothing but stockinette stitch and that would get kind of boring after a while.
From the way you have the pattern listed above, it looks like you are just knitting those first 8 rows. It sounds like the pattern begins with a garter stitch border. Garter stitch is the result you get from knitting every row for two or more rows. It looks like a series of horizontal bumps going across your rows and it looks like that on both sides.
Stockinette stitch is what you get when you alternate a knit row with a purl row. At least when you are doing it flat. One side of it will look like a series of V's next to one another going across and the other side will look like a horizontal series of bumps.