In the Silmarillion, the universe was created by the music of the Ainur. At first it was in line with the mind of Iluvatar (God) but Melkor sang louder and then in discord. Some fans theorize that this discord created Tom Bombadil, along with barrow wrights, Shelob, the watcher of the water, and the ancient creatures that Gandalf saw while chasing the Balrog under Moria.
The barrow-wights are undead, things that were once living humans and were buried in the mounds they haunt. They're not primeval beings.
Shelob has a canonical origin story, as I recall, as daughter of the primeval spider-shadow thing Ungoliant. The watcher in the water doesn't seem quite spectacular enough to be truly primeval if you ask me, but then again, Bombadil isn't especially flashy either, and we know he is primeval. Maybe it's more relevant that the watcher in the water wasn't always there, it only appeared around the same time as the balrog was dug up. Which sounds pretty un-primeval to me.
