Precognition has existed as a psionic ability in D&D since OD&D, and the AD&D text is almost (but not quite) an exact copy of the OD&D text. How it actually plays out in-game is not detailed very well. This page aims to fix that.
If option A is selected, if the private accuracy check passed, then the gameplay that was done is considered to have really happened. It is “solidified” as reality, and gameplay continues immediately following the events covered by the precog. But if the accuracy check failed, then when the party acts on the precog (e.g. opens the door), the group would have to play out the event again, complete with all-new combat, dice rolls, whatever, AND the party might find that facts are different than seen in the precog, since the DM might have made some stuff up due to the failed accuracy roll.
If option B is selected OR if any factors change (e.g. the party goes and does something else first, or the party casts spells, or basically anything that could alter the future), the precognition is thrown out.
It would be great if the precog accuracy check could be made publicly, but I don't see how that could be possible. It seems like it needs to be made privately, like trap detection, hear noise, and augury.
This is a pretty powerful ability since it can function effectively as a wish in some cases, able to throw out the results of a bad combat. The accuracy roll balances it, as well as the cost of session time – players overusing precog could burn through a lot of table time throwing out lengthy precog results.