You have to adjust from round to flat knitting. In flat knitting stockinette stitch is accomplished by knitting one row and purling one row for the pattern. In the round, you knit all the rows to achieve stockinette. It has to do with the fact that you're not turning your work in the round, so it comes out differently.
So, when switching from round to flat, you have to figure out which stitch you want to achieve and do what you need to do to get it. If the hat calls for stockinette and says knit every row, you'll know that the st. st. is what's important, so you'll knit one row,and purl one row.