According to the Oxford American Dictionary, animism is
The attribution of a soul to plants, inanimate objects and natural phenomena
Ultima is a curandera, the modern day equivalent of a medicine woman or shaman. While the dominant religion of the region is Catholic, traditions and beliefs have survived from the days of Native animist religions, and Ultima has preserved them.
Her "power animal" so to speak, is the owl, and her spirit is bonded to it. This is why Tenorio kills the owl towards the end in an attempt to kill Ultima, after he discovers this secret.
Ultima's healing rituals, using natural herbs and plants gathered and prepared in the traditional ways, attempt to expel evil spirits and illnesses, as well as counter curses placed by Tenorio's bruja (witch) daughters.
All of these are examples of Ultima's animist beliefs and practices.