I almost posted a response along these lines: how distinguishable are precognition and time travel from a fundamental physics perspective, anyway? It's all about information flow.

But then I realized that precognition has an alternate possible mechanism: rather than extracting information from the future, it could operate by sensing the initial state/initial wavefunction of the surrounding universe and integrating the equations of motion forward in time to predict the future state (perhaps probabilistically). That would presumably require some amazing new physics just as significant as time travel, but it wouldn't be the same new physics.