I purchased this set a couple weeks ago (from here on itch.io), just now getting it into Tiled to work with. It seems to be missing the two lighter background tile variants. There are two 6-section patches of the darkest of the backgrounds (the shade you use for shallows around your island in your sample pics here on this site), but none of the lighter two shades (the deep water, and land shades from your sample pics). The two lighter shades are present in combining tiles, but not as background-fill tiles.
Is there some trick to this that I'm missing?
[Edit] I downloaded one of your sample maps, and extracted the missing background tiles from it. Seems to be good enough for now. Hope that's OK with you...