You ask what Schuon may have meant (in Logic and Transcendence) when he distinguished between “the traditional theory of emanation” and “the emanationist heresy, which has nothing metaphysical about it and which reduces the Principle to the level of manifestation or Substance to the level of accidents” (p. 58, note 11 of my edition).
As you know, Schuon always specified that “God is in things and things are in God” essentially, not substantially. Since it is in the very nature (or essence) of the Good to communicate itself, God cannot but “radiate”, and this radiation constitutes what we call manifestation or creation. Nonetheless this manifestation involves no division or extrusion of God, as if He were some sort of extended “thing” or “substance”, quod absit. He remains, His self-communication notwithstanding, completely transcendent, hence absolutely other than everything else.
Thus, as I understand the passage in question, “the traditional theory” points to God’s essential presence in manifestation, while “the heresy” makes the mistake of supposing that God is substantially present. It’s the difference, in other words, between panentheism and pantheism.
Perhaps the following observations, coming from two Christian Platonists living several centuries apart, would be helpful here:
“In a super-substantial manner, above the category of origin, the Godhead is the Origin of all origin and the good and bounteous Communication (so far as such may be) of hidden mysteries; and, in a word, It is the Life of all things that live and the Being of all that are, the Origin and Cause of all life and being through Its bounty, which both brings them into existence and maintains them. These mysteries we learn from the Divine Scriptures, and thou wilt find that, in well-nigh all the utterances of the Sacred Writers, the Divine Names refer in a Symbolical Revelation to Its beneficent Emanations” (Dionysius the Areopagite, On the Divine Names, Chapter 1, my italics).
“I know that to create is defined as ‘to make out of nothing’, ex nihilo. But I take that to mean ‘not out of any pre-existing material’. It can’t mean that God makes what God has not thought of, or that He gives His creatures any powers or beauties which He Himself does not possess. Why, we think that even human work comes nearest to creation when the maker has ‘got it all out of his own head’. Nor am I suggesting a theory of ’emanations’. The differentia of an ’emanation’—literally an overflowing, a trickling out—would be that it suggests something involuntary. But my words—’uttering’ and ‘inventing’—are meant to suggest an act” (C. S. Lewis, Letters to Malcolm: Chiefly on Prayer, Chapter XIV).
It seems to me clear that the Areopagite is espousing “the traditional theory”, whereas Lewis is referring (at the end of this passage) to “the emanationist heresy”. Notice that Lewis adds one other important qualification: namely, that the heresy in question construes the creative process as mechanical or automatic, while Schuon and other “traditionalists”, though they underscore the inevitability of manifestation, do not divorce it from the Divine Will.