Anyone trying to implement the Tiled API probably needs to reference this: https://eishiya.com/articles/tiled

It's a bit vague in some places (I'm still not exactly sure how parallax is supposed to be implemented) but absolutely worthwhile.

I'm not sure if it's the proper method, but I actually did implement parallax in my project, though I just did it by essentially creating a layer which I marked as parallax and then had my game draw it with a parallax offset from the rest of the map depending on the camera position.

https://doc.mapeditor.org/en/latest/manual/layers/#parallax-...

These docs do seem to go more in depth about the canonical values related to parallax that Tiled offers though.