Having played in the pre-owned market for years, it's been a long time since I've had a NIB watch from an AD, but I can speak from experience having had my Tudor's serviced.
I used to be a non believer in a 'break in' period, but I've noticed from a year ago that my Tudor with the ETA 2824 did indeed change from being a couple of seconds too slow per day to +3-4 after a couple of weeks of wearing. My own experience is further impacted by the fact I have 4 watches worn in rotation and the non worn watches live on a winder, where the timing tends to go a bit fast.
I would say to be patient...give the watch a full wind a couple of times a week if this is the only one on your wrist, keep track via one of the on line timekeeping sites and see where it goes after a couple of weeks. You're looking for consistency, so if the watch continues to run faster than you'd like, but consistently at the same pace, then you've got a watch that just needs a slight tweak, which under warranty should be nothing more than a time inconvenience.