I just noticed that the example map in the mod folder has the tilessets + bitmaps copied there which have a directory structure which looks like it would work with Tiled.

I went ahead and tried to use the tilesets in the mods folder but got the following error when trying the map (probably the first one it tried to load that I used in the map):
Error loading map: Unable to load or parse sourced tileset:
tilesets/ridges/Stone Lava - ridge2.tsx

Obviously its pointing to the wrong location. I'm not sure why tilesets is being added to the location, it doesn't have that in the file location for the tileset or any images in Tiled.

I also tried to open a map in the official maps location under the steam directory (not mods) and Tiled failed to find the tilesets, showing an error about it.

Any ideas?

Ok, so I figured out that the tileset in question is a duplicate broken tileset in the mod folder that isn't in the main assets folder. I replaced the tiles with the working tileset and deleted the broken one from the map and it loaded.

Still seems like something broken when using Tiled with tilesets loaded/imported from assets folder, but for now this will work.