Ayahuasca !

They drink ayahuasca. The film is full of references to ayahuasca, for example the wooden sticks on the altars are large banisteriopsis caapi sticks and lots of shipibo textiles and art everywhere in this film. (And no, shipibo don't live in this area, but that's not important in this film. It's all symbolism.)
The black vomiting is also very typical for ayahuasca as well as the snakes and the primitive animal visuals.

The film also shows peyote, which has a long history of ritualistic and medicinal use by indigenous Americans. The use of peyote is rather common among indigenous Americans and thus it's not the 'secret experience'. The secret experience is ayahuasca.