It appears tmxrasterizer can only render .tmx maps with .tsx tilesets. If you try to use it with a .json map it will output
Error while reading "mymap.json": Not a map file.
Since I work exclusively with .json files I ended up having to temporarily export them to .tmx using Tiled command-line, then call the rasterizer. It works but I found it odd that it wouldn’t support .json files.