Welcome to the forum Ben.
What you describe is most cerainly a loose hand, I have had this problem with a couple of watches purchased from EBay. The movement will have to be removed from the case, and the hand pressed on again. I have one myself that is in bits at the moment. The chrono hand was that tightly fitted that the hand separated from the tube it is mounted on, luckily I managed to track down a new one. They are lovely watches!