The Psychic gets called a giallo movie a lot of the time, but to me it's sort of an inverse of the genre. A lot of giallo movies (especially the ones by Dario Argento) involve the hero trying to recall details of a crucial memory, but Lucio Fulci's The Psychic deals instead with a hero who is tortured by psychic visions, the chronology of which is uncertain.
Unlike the movies that Fulci is now famous for, there's very little gore or even just blood in The Psychic, with Fulci opting instead for subtly hallucinogenic effects that might remind you of Don't Look Now, which is also about psychic premonitions and also features the color red as crucial to its plot.
Unlike Nicholas Roeg, though, Fulci unfortunately has a lot of fairly dull mystery exposition that he has to keep in the movie, although I'll be damned if I can imagine anybody being too invested in the plot of a movie like this. As always, it's all about sensations - in this case the sensation of trying to piece together a murder that happened in your head before it happened in real life (if it happened at all).
You might be able to tell that I'm tap dancing around the actual plot of this movie, and that's because it all hinges on a couple of big twists, all of which are pretty satisfying even if you get lost in the details of the central investigation. And Fulci's infamous nastiness does poke its head out a few times, although nothing on the level of The New York Ripper, Don't Torture a Duckling, or his zombie movies. Definitely check it out if you're interested in giallo or the thriller genre in general, particularly if you're interested in Fulci but don't like watching people's flesh get torn off in creative ways.