So, I heard this phenomenon named yesterday on this blog post from "The Spirit of Error" website, which kind of says all you need to know about the OP.
I didn't link to the site just because.
The blog post that irked me the most is entitled (and linked here) How to Spot a NAR Book
Later in the Facebook feed where the blog post was linked, there was also a link to a book critical of the movement entitled New Apostolic Reformation? (or NAR, for short).
So, I bought it and read through the first two chapters last night that defined the topic and the context of the critique as well as a little later in the book that criticizes the Seven Mountain Mandate.
This last bit surprisingly lumps Loren Cunningham and Bill Bright into the crosshairs of the critique. In short, these two leaders sought to focus on the seven peak influencers in a community. Ironically, the criticism says nothing about Abraham Kuyper's (horrifying) notion of "sphere sovereignty" which is exactly the same thing, just another way to talk about a form of Christian colonizing rather than inviting the Kingdom to come through strangers and exiles (Hebrews says something about this in chapters 11 and 12).
In summary, the New Apostolic Movement is identified with C. Peter Wagner of church growth guru fame as well as another 20th century movement called the Latter Rain. Similar movements are named including African Independent Churches, The Kansas City Prophets (cool name for a band, I think), the Latter Day Saints (Mormons), the Bethel School of Worship, and the International House of Prayer. (Do I have your attention now?) Note: I have avoided hyperlinking in this paragraph because you can just google any of these topics on your own. The main contention against NAR is that all of these groups point toward modern-day apostles and prophets.
My initial worries about critics of NAR:
When I read more of the book and its critiques (such as not knowing anything about the Latter Rain movement), which could take some time with the semester starting Monday (and because I should be working on my syllabi instead of writing this), I'll try to post some updates later.