Timing Lag

[Cornellref]

As the offical calls a violation he/she glances at the clock. The clock shows 45 seconds but the timer stops the clock showing 42 seconds. Offical instructs the timer to reset the game clock to 45 seconds because he/she had definite knowledge of the amount of time involved. Is the official correct?

As an aside lets say the timer stops it at 35 seconds What would you do in that situation. Of if the clock malfunctions and runs to zero. Thanks - Josh