In Blitz under FIDE rules, Player A makes and completes an illegal move by pressing the clock. Player B states that Player A's move is illegal, does not make a move, but quickly presses his own clock, as if giving Player A the opportunity to correct the move as common in a standard non-Blitz game. Almost immediately, before any other action by either player, Player B realizes that the rules of Blitz apply, stops the clock, and claims the match.
According to Player A, the claim is now "in his time", so is no longer valid. Is this a correct interpretation of the rules?