The Nell drop targets have two modes. There is one mode that is triggered by dropping all of the targets once and then you have to hit one more target to collect the 25 Million points (or 50 if you've started it a 2nd time). This mode is timed and last for 15 seconds or so, and will use the log mechanism, and the mode sound is the narrator of the show talking about time ticking down.... "just in the nick of time!".
There is another mode called Nell Drops. Its part of the modes you can start through the puzzle pieces you collect, and might also be available through a mystery award... in this mode Nell is tied to the tracks and you need to hit the drop targets as many times as you can to collect 2M points each before the timer runs out. This is the mode where Nell says SAVE ME SAVE ME. The log mechanism doesnt run in this mode (at least on my machine), and that sort of makes sense, since in the story in this scenario she is tied to tracks, not the log.