Hi Darcie. The arrival time is just that -- an expected arrival time into the port. It takes at least an hour or two to complete all the paperwork required to clear the ship back into the States.
As far as passenger disembarkation, that is usually done in several phases. First, passengers who want to carry ALL of their luggage off the ship are typically allowed off first. This is optional, and something I've never done as I have too much luggage to handle.
Otherwise, the ship will provide you with color- or number-coded tags, and disembarkation is done by color or number. In my experience, we've gotten off the ship anywhere from two to four hours after docking. I am not familiar with the specifics of Royal Caribbean's procedure, yet this is how most lines do it.