The synopsis are misleading, first of all: you need to understand that this movie is categorized under "sci-fi" which is very wrong.
It's pure drama, romance... maybe with a bit of fantasy, but no science fiction at all.
No time traveling, no reincarnation..
It's not - as all reviews & synopsis tell - about three characters living in three different times!
*(spoiler)*
There's only one real character in this film, which is the doctor "Tommy" who's desperate to find a cure for his wife's cancer before it's too late.
The other two characters (the conquistador & the bald monk floating towards xibalba) are both fictional characters created by the wife "Izzi" in her book that carries the movie's title "the fountain".
It's a great film, worth watching,
The soundtrack in particular was remarkable, and I think it's the main effective factor in the film.