C3's support for TMX files was from before TSX files even existed. Before that, tileset information and tilemap information where all in the same TMX file.
At one point it was brought up that some people were not able to load TMX files generated by the then latest version (can't remember the number now) of Tiled, and it was because TSX files were introduced and the new default was to generate separate files for maps and tilesets.
I would need to check it to be sure because I haven't seen that part of the code in a while now, but I think that the importer checks the TMX file and if it finds tileset information in it, it uses that. If it doesn't, it needs it to be provided in a separate TSX file. That's why the tileset input is labelled as optional.
I don't know exactly how it is in the latest version of Tiled, but last time I checked when you created a new tileset there was a check box named "Embed in map". When ticked all the tileset information is stored in the TMX file and if not it is separated to a TSX file.
If you want to embed a tileset there is a button in the Tilesets pane to do that, I imagine that just pressing it will make it so that saving the tilemap will generate a new TMX with all the information.
If you have an embeded tileset and want to remove it, there is a button to export the tileset into a TSX file, after exporting it you can use the option to replace an existing embeded tileset with the external one.