"5. Generate the Parallax FX (incorrectly, the result uses old version of layers from the original sprite)"
Uses the old and new version of the layer. Both two. It puts it one after the other. I believe the rest of the steps are correct.
In fact, I close Aseprite, open it again, try again and I get the same error. Restarting the PC as well.
Also, I copy the layers into a new document and try the effect and I still get the same error. It is as if the layers themselves keep a history of changes.