You'll be using an internal water pan (disposable foil pan partially filled with liquid) snugged up next to the smoke box when you smoke butts. Some drippings will drop off the top of the smoke box and go into your internal water pan, and some drippings will drip to the bottom, and go through the hole in the bottom into the drip pan that slides underneath. I'm not sure why you are using an AMNPS with your MES, other than the built-in smoking option is inadequate, which is not surprising I guess.
In the SI, an AMNPS is not required unless you are cold or low-temp smoking, but for cold smoking, an AMNTS is often helpful. Personally, I use the SI cold smoke plate and chips for my cold smokes, but many have found success with the AMNTS.
With the SI, you put in your chunks, and that's it, until done. Get some sleep, or go do something else until your meat is done.