Can I use a fast track services at Sanya Phoenix Airport for checked luggage, or do I need to check in first?

First, handle the check-in procedures at the counter (if you need to take a luggage claim, handle it simultaneously with the check-in procedures), and then go through security.
First, complete the check-in process at the counter (if you need to have luggage transported, do it simultaneously with the check-in process). Afterwards, security check.