Good explanation Sojourner. To expand on this a bit;The decel popping is a result of super-heated unburned fuel that exits the cylinder head on every exhaust stroke and comes in contact with oxygen. This happens mostly on deceleration. If the fuel/air ratio is right the unspent fuel will combust. Find the air leaks be it at the exhaust gaskets, the PAIR system or the makeup of the exhaust system where the pipes slip onto each other. If you have an unbaffled exhaust system that's considered a "tuned" exhaust then air can be pulled up the pipes after each exhaust pulse and bang.
The solution is to change the fuel/air ratio on "zero" throttle so it's too rich to fire off. The PC allows you to do that.
When fresh air is pulled back up the pipe from the exit, that is reversion. Well designed exhaust absolutely minimizes this to the effect of better low end power. There are things that can be done to the exhaust to minimize that as well. One reason "open exhausts" hurt bottom end power. Sometimes noticeably so.
There are 2 fueling strategies that help. One is to shut off the fuel entirely at zero throttle so that there is no fuel in the exhaust to ignite. The other is to increase the amount of fuel during decel so that, as you pointed out, the mix is too rich to burn. Both work to different effect on different hikes for different reasons. For the VTX, the most common is as Sojourner points out, is to add fuel at decel. It seems for Harleys, in my experience anyway, it's common to kill the fuel during decel.