I have the same problem with FFXIV on my RX580 on the new Adrenalin-Edition-18.4.1-Apr26 drivers. The problem goes away when I change to full screen mode moving away from borderless windowed.
As you highlighted the issues occurs from the frame pacing and border-less windowed mode. Which bites.
I have a Gigabyte rx 580 8g xtr. The frame rate limiting for Final Fantasty XIV is still not working in borderless windowed mode with AMD drivers 18.5.1 and 18.5.2.
Also if I allow FFXIV to run without frame rate limiting my Gigabyte rx 580 8g xtr on any of the new drivers (18.4.1 through 18.5.2) FFXIV will sometimes crash to the desktop. I don't have any other games that do this (I play Overwatch, Dauntless and a few others).
So I'm continuing to use the 18.3.4 driver for now.