Adamantine, yes, the distinction between terma and other re-presentation is worth being clear about. (Although, according to Guru Chöwang, ultimately, all Dharma is terma.) My characterization of the list of 1980s developments as "termas" was a slip, inasmuch as Tarthang Tulku's work was not one. (The others were, or at least claimed to be). Likewise, I do not mistake any of the current new Western developments as terma, nor do they present themselves as such.
Also, I do not endorse any of those developments. For instance, some of Shinzen Young's introductory talks about Vajrayana on YouTube are admirably clear and seem accurate. But when he talks about practicing the Virgin Mary as yidam, I go "Yikes! Whoa! That is way
beyond the pale for me, personally." But I don't know for sure
that it can't work...
What I'm excited about is that the cultural climate seems to have shifted so that tantra is no longer being effectively suppressed by the Consensus. That should be good for strictly traditional tantra as well as possible new developments.
Re leaving emotions as they are: I do not see the contradiction between the two passages you cite. Düdjom Rinpoche confirms that this is the method of Dzogchen; he then points out that you should not claim to be able to apply that approach unless you actually can.
Who gave the transmission of this lineage to the Aro leader?
Aro Lingma, the original terton, in visions.
Obviously, this is not verifiable. But neither is the reception of any other dag snang gter, all of which are revealed in this way. (The Düdjom Ter being another relatively recent example.)
he explicitly rejects karma and rebirth
Uh, no. Are you referring to "No cosmic justice"? That doesn't reject rebirth or karma at all. (I understand that it could easily be misread that way if you start from the assumption that anyone who isn't altogether traditional will hold all modernist prejudices. Maybe it needs some clarification and expansion.)
The page explicitly endorses a particular notion of karma, and says nothing about rebirth one way or the other. The point is that there isn't an external, eternal mechanism of reward and punishment.
The Aro Lamas teach rebirth explicitly and say that, at minimum, you need to have an open mind about it if you are going to be a student. (The Aro bardo teachings wouldn't make much sense without that, would they?)