It unfortunately does, and I'm really not sure how to deal with these as I've had similar propositions for my other tilesets before. Maybe make it so that it requires the assets to be placed somewhere manually?
I am using this tileset in a commercial game and plan to ship a level editor, but allowing for full customization of the level background would be redistribution as you've defined. Having the user import a resource wouldn't quite work either, as the game relies on a modified version of the tileset.
Any ideas on how I can approach this? Worst case scenario I can just remove background customization from the editor, but I would definitely prefer to allow it somehow. I would be willing to explore licensing options, e.g. giving you a cut of sales or paying up front.