There are literally countless examples of this from the 1960s - early 1970s in British film and TV. This actually had real world consequences: in Haiti, Papa Doc Duvalier's Tonton Macoutes used this belief in voodoo to help cow the population and keep him in power.
Taking the strange and unusual and using it to thrill, frighten, and/or entertain is not limited to voodoo. For whatever reason, that particular brand of the unfamiliar was being used in the period you observed. Who knows why exactly? A lot of writers pull from stuff they've read or learned of beforehand, so maybe Fleming (or whoever) read some article about voodoo or was vacationing in a place where voodoo was practised and the writer got intrigued, maybe a little spooked out...
Papa Doc used filmmakers' voodoo to impose fear on his people? Or was voodoo already prevalent there?
It was prevalent before, but Duvalier took it to a new level to hold onto power. Western film-makers suggesting (even if only tongue-in- cheek) that there "might be something to it" did nothing to diminish that.
Okay, but was he screening these films? Your original post implied that there was a direct causal link and I'd like to read that article or research paper or something.
It's a fascinating way that film has/had an effect in the world, and I'd love to read more about it.