Hi,
Yes, there are huts. We've only been in Dec. and we did "reserve" our hut fairly early (by 7:30). We wanted a particular area near our room but if you're willing to walk the beach for a bit the huts between Divi and Tam didn't fill up as quickly. There was little shade around the pool area, just a couple of canopy type things that were fairly hard to get. Have a great trip.