Well, I was curious who was right in this debate. So since SnapShot is the main pre-emergent we install, I contacted Dow AgroSciences, LLC (the manufacturer) and posed this question to them. The question being; whether it's best to install the Pre-M underneath a layer of new mulch or on top. Seems that either application is acceptable. But it seems that you do not need to do both. Here is the exact reply I got from "Jenny" with Dow;
Thank you for contacting Dow AgroSciences. It can be done both ways. We always tell folks if the mulch is not down yet, go ahead and apply SnapShot* first. If it is already down, just make sure you are watering it enough so that it gets incorporated into the soil.
I hope this helps!