I don't understand what the issue is/could be. "Respectively" is clearly functioning syntactically as an adverb, and the sentence "Bob, Alicia, and Siobhan are a teacher, plumber, and electrician" without the "respectively" is a valid sentence where its two noun phrases happen to be conjunctions of other nouns.

A sentence like "Bob, Alicia, and Siobhan are a teacher, plumber, electrician, and an astronaut, respectively" is equally valid syntactically, it's just invalid semantically.