What exactly happened with Minthe and Hades in the legend?

It depends on who is telling it, and it’s always the Romans who do.

In one version, she claimed she was more desirable than Persephone, so Demeter turned her into a mint plant, and in another, she was turned into a mint plant by Persephone for attracting her husband’s attention.

I wrote quite a bit about Minthe here if you’re interested, including a whole lot about my feeling on syncretism and the Romans.