As Ramchal explains in his comments here, there is in fact no contradiction in the depictions offered in EitzChaim cited above. For, when it comes to the Lights under discussion here, “aside from (considering) the sources from which they emerged, we must also take into account the sources to which they’re (eventually) bound, and from which they derive their power and governing ability”.
So we need to know that while “these Lights (originally) emerged from the ‘eyes’, they were then bound to Adam Kadmon’s Malchut and they (likewise) derived their governing ability from there.”
(c) 2013 Rabbi Yaakov Feldman
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