There's also quantum mechanics and relativity to take into account.
With quantum mechanics there is time symmetry. e.g. at the molecular level there are experiments where doing something 5 minutes from now changes what readings you get 5 minutes before now, not the other way around.
Also, with relativistic time dilation, anything traveling at the speed of light experiences zero subjective time. e.g. a photon emitted at one point and absorbed at another point considers that to be the same exact time, not past and future. A classic experiment that expresses this is the photon double-slit experiment where whether there are one or two slits later, then the photon knows what path to take before. In these types of experiment, the photon seems to paradoxically "know" it's future at the moment it was emitted. That's resolved by understanding that time is relative. What is "past and future" in one point of reference is the same point in time according to another point of reference.
So the thing with prophecies, if they were at all possible, is that they don't follow classical newtonian physics common sense of cause and effect, they'd follow the weird "there is no such thing as the present" logic of quantum mechanics and relativity.
In a setting where information can flow backwards in time it makes no sense to adhere to a classical physics idea that only past causes are allowed. The prophet is only tapping into that backwards information flow, the information flow was already there, meaning the future in that setting already affects the past, so there is no contradiction. Causes can be in the future.