For as long as I can remember, the "official" check-in time at H2 has been 3pm and the check-out time as noon. That's pretty much the same as many other resorts, not just in Jamaica. I've found that at most resorts, those times are guidelines and are flexible at the discretion of the front desk staff.
I agree with Denny, and not only for other resorts. Pretty much all
hotels have a check-in time that's a few hours or more after check-out time. Otherwise you'd have overlap and that just plain won't work. You can't expect them to give you a room when the previous batch of guests haven't been required to leave yet. It's not about courtesy or customer service; it's about logistics.
That said, most hotels will let you onto the premises as long as you have a reservation starting that day, will take your luggage to the bell station, and will let you roam the common areas until your official check-in time rolls around. It only makes sense for Hedo to get back to that policy.