Perhaps because I’m quite familiar with Beeminder, it’s hard for me to tell exactly what part of this doesn’t yet make sense. But at least I can try to sketch out an overall mental model that might be helpful.
Ratcheting deals with the future, not the past. It’s not going to rewrite history—but it’s going to change your obligations starting from today. So, as you can see in the GIF you made, everything before today stays the same, no matter what. The datapoints stay the same, of course, but also the road stays still in all the segments up to today’s.
The entire future part of the road, however, is “lifted up” by an appropriate amount. It’s translated on the Y-axis: it doesn’t change it’s slope or anything else, it’s just that bit higher.
What this means is that there will be a step-discontinuity on today. That is, the road jumps up vertically, to bridge between the two section described above.
That explanation should be complete—every other change you see can be derived from it, I think. It might be that the colors are what’s confusing, but they shouldn’t be. The colors (both today’s, and of historical data points) are computed based on how distant they are on the X-axis from the bright red line. That is, if you extend a horizontal line (a line parallel to the X-axis) from a datapoint, what distance along that line is the intersection of that line with the BRL from the the datapoint? That’s a number measured in days (because the X-axis is measured in days. If it’s 3 or more days, the datapoint is colored green. If it’s 2 days, then the datapoint is blue, if it’s 1 day the datapoint is yellow, and if it’s zero (or negative, that is, the datapoint is on the far side of the BRL), the datapoint is colored red.
It should now be clear how and why the colors—both the color of what’s required today, and also the color of yesterday’s datapoint—change as you ratchet the graph.