My answer is going to be no, this is not entailed - and further that the nature of the evidence/ experience of precognition is evidence against the future having 'already happened'.
I have often seen it stated that precognition - for example visions in dreams that predict the future - entails that the future has 'already happened' - either because everything is pre-determined and merely unfolds, or else because Time is simultaneous rather than sequential.
Therefore, evidence of the reality of pre-cognition - for example evidence to support the reality a prophecy, or foresight, or precognitive dreams - is taken to be evidence that the future has already happened, and that this already-happened future was somehow glimpsed by the precognitive prophet.
Of course, many/ most people who write in the public domain deny the reality of precognition altogether and dismiss the evidence for its occurrence. However, this denial and dismissal is a minority view, very unusual in the modern world and almost unique in world history: most people have done and still do believe in precognition; and many people have experienced it in their lives.
So I will assume that precognition is real, and look at the nature of the evidence for its reality. When this is done, it seems to be the pattern that precognition may be more-or-less precise in the specifics of what happens, but is always imprecise, vague, non-committal about the exact time and place and circumstances in which the prediction will happen.
This fits with the idea is that true precognitions and prophecies are made-to-happen in the future (presumably by some supernatural entity or force) - and not that that have 'already happened' and are merely being read-off.
It also implies that God (or whatever makes the thing happen) is constrained by free will and other contingencies. Such that the thing predicted will happen, but the exact time, place and circumstances are flexible - depending upon individual choices and other circumstances.
So, the prediction is that 'sooner-or-later this thing will happen', by some means or another, to some person or another - but that it can be brought forward, delayed, made to happen in one place rather than another, and so on.
This, I assume, is why even true and correct prophecies nearly always turn-out somewhat differently - sometimes surprisingly differently - from how they were imagined; because circumstances and choices dictated that that was how they had to turn out.
1. Experience, evidence and the consensus of mankind confirm that precognition is sometimes real.
2. The nature of the real and reliably-reported experience of precognition implies that some future events can be foreseen, but not located precisely in time, space and person.
3. Therefore, the evidence is exactly consistent with what would be expected if the future was not fixed: and that the future can be made to happen, but only within constraints that determine how and when it happens.
4. In a nutshell: Evidence seems to suggest that the occurrence of some future events happens may be fixed; but how and when it occurs is un-fixed.
5. Our experience is that future - while specific elements may be predictable - is essentially open, undetermined, contingent - presumably (at least partly) because of the reality of free wills which really are free, hence unpredictable.