Originally there was the Mountain Pass mine, and China setup their own mines while also building out the refining and processing capacity. Until recently MP Materials was shipping all it's output to Chinese refiners.

The history and asset ownership is also quite convoluted. Try this Wikipedia article:

https://en.wikipedia.org/wiki/Neo_Performance_Materials

This article is quite good at explaining how China cornered the market:

https://thehustle.co/originals/what-the-hell-are-rare-earth-...

The article explicitly says that the magnet manufacturer was bought by a shell company owned by chinese interests, which lied when they pledged to develop the activity.

Not that it's very surprising (US companies routinely do this as well, especially in Europe), but in this case it had clearly an ulterior motive.