adverbial Clause: He came when he had finished with the work.
"Practical Grammar and Composition"
Thomas Wood
It must not be confused with an adverb or an adverbial modifier.
"Practical Grammar and Composition"
Thomas Wood
"Westover is no longer an adverbial phrase, even qualifying the verb 'to go,'" said Barbara, exultingly, looking abroad upon the family settlement, to which our new barn, rising up, added another building.
"We Girls: A Home Story"
Mrs. A. D. T. Whitney