In short, how would you know the difference?
For the sake of argument, we’ll assume time travel is possible and any nasty paradoxes created by doing so are of no consequence. Also, we’ll have to assume that psychic prediction of future events is accepted.
If you traveled back in time (assuming you kept your memory, unlike Quantum Leap) it would appear to the people of the “past” that you had the ability to predict the future. You ought to have beforehand knowledge of any event that happns up until the time you traveled back.
Looking at it from the other direction, the ability of someone to predict the future could be explained equally well by psychic abilities or by the possibility that they are a visitor from the future.
Either phenomenon results in the ability to prognosticate. It seems to me that it would be impossible to distinguish one from the other.
So, if someone else can predict future events, how could you tell if it were a feat of prophecy or a result of time travel? If it were you who had this ability—and for some reason, you couldn’t remember travling back through time—how would you know which explanation was correct?