Here's how it works to put you at ease.
When the plane lands at OIA and the bags are transported off the plane all bags with the Yellow Mickey tags are pulled off and sorted seperately. They are scanned by the DME folks at the airport which alerts them to which hotel the bags need to go to. They are put in baggage "cages" by resort, loaded onto a truck and then transported to your hotel. When the cages are brought to the luggage room at the hotel the cages are unloaded and the bags are sorted by name (which are on your tags). The bags are then scanned to know what room the bags need to go to. Then, as long as you have arrived (which at this point you should have as it takes you a lot less time to get to the hotel than your bags) your bags will be brought up to the room. Each room has a scanner which is scanned by the bellman to let the hotel know what bags were placed in what room. This helps if by any chance your bags were delivered to the wrong room (which doesn't happen often), we still know where they are and can move them for you!
Hope that helps you in understanding the process and feel a bit better about using the service. It's a great perk for resort guests and I highly recommend it. Just remember as others have said, it can take up to around 3-4 hours for your bags to get to your room so ensure you pack anything you need (including medication, sunscreen, bathing suit, etc.) in your carry on. If you have any other questions about it, please feel free to ask!