In garter stitch, you have ridges of purl on both sides.
In stockinette stitch, the purl bumps are on the inside and the v's are on the outside.
In reverse stockinette stitch, the bumps are on the outside and the v's are on the inside.
I think the terminology is what's confusing me. You can't get garter stitch in the round unless you purl a round. I suspect that you've got stockinette for part of your hat and reverse stockinette for the other part. It has to do with were you're needles are. You should be knitting on the outside of the hat to get the v's all on the outside.