Parody tag is generally used for re-creations (redraws, slightly different dialogue, etc) of a work or part of a work. The OTOMAD itself likely parodies the original work, but unless the art itself recreates or "parodies" the original work or a specific part of an original work in some way, I probably wouldn't use the parody tag.
For example, you don't tag every fanart of a character or series as a "parody", but you might tag a specific scene or recurring joke regarding the character or series as "parody" (yamcha pose (meme) or sailor moon redraw challenge (meme) are good examples).
A more complex example is Cookie☆, for which many OTOMADs are made, and there exist endless, endless cross-references and memes. Parodies are made from source material, and more parodies are made from these parodies.
See parody wiki page as well, which describes the concept quite well.
Unrelatedly, I'm now wondering at what point a parody becomes so widespread that it stops being a parody and starts becoming a meme. Hmm.