I've never heard of a pro-adjunct, but I've heard of a fused relative, so I would have called it a fused relative.
The reason that he erupted in rage = Why he erupted in rage
Why is the fusion of
the reason and
that.
(that is a relative pronoun.)
The analogous structure is
That which he said = What he said
What is the fusion of
that and
which. (
which is a relative pronoun.)
Fused relatives contain the antecedent and the pronoun within the same word.
Does that make sense?
CJ