Is this classification of mineral formation environments correct?
A genetic classification.

Endogenic: Magmatic, Metamorphic, Hydrothermal
Exogenic: Supergene, Sedimentary

For more on this please see Wenk, H. R., &amp; Bulakh, A. (2016). Minerals: their constitution and origin. Cambridge University Press (second edition) 
or the first edition of this book(2004).