It's not right. You might not be pulling the old st off the needle completely, so it combines with the new st to make the X. Take a bit of scrap yarn and practice the ribbing for a bit until you figure out how you're getting the X and how to fix it. Right or left handed should make no difference, but if you're a continental knitter with the yarn in the left hand, the purls are a little more difficult I've heard.
sue- knitting heretic