[Nevadaref]

Sorry, Tanner, you are incorrect. The name and number of the player must be added to the scorebook and a team technical foul must be charged per 10-1-2b.

Pay special attention to the penalty section of that article. It specifies when you penalize each of these five items. Only (a) needs to be caught before the ball becomes live.

PS After checking the case book play that you cited, I see why you were confused. What the case book is telling you is that you must penalize this at the time that the scorer makes the change. If you tell the scorer to make the change, but for some reason fail to assess a T right then, you can't go back and charge it after the next live ball. It is a now or never thing. The proper time to penalize is during the dead ball when the scorer bring this to your attention. That was the case in your situation, so you should have assessed the T. However, according to the case book, if the opposing coach had pointed out your error two minutes later, then by rule you have to live with it. Make sense?