Thanks so much everyone! I think I have in fact been doing this inside out. It should be OK with the hat I've already knit, but I guess I should start doing it right.
Another question: what's the advantage/disadvantage to using double point needles vs. circular needles? The woman at the shop where I bought the yarn was pretty insistent that I use the double point needles. But the circular needle seems like it would be a lot easier. Any ideas?