The policy allows the judge to take context into account, so they have three options: rewind, partial fix, or leave as it is.
If the judge feels confident that they can rewind to the point of the mistake, because there is no new information and they can restore the game to the point where the second ability from Burn them All would be on the stack, they can do so.
In this case, with attacks and blocks declared, there seems to definitely have been new information, so unless I'm missing some context I disagree with your comment that there was not.
If the judge cannot rewind and a partial fix would restore the game state, they can apply it. Here, destroying Burn Them All seems like a reasonable partial fix.
Nic not being responsible for their opponent's triggers just mean that Nic doesn't get a penalty, while Tyler does (likely upgraded in a Warning, as missing this trigger seems quite in Tyler's advantage, but again, the judge needs to consider context for this).