exactly vs on the nose

exactly is not an adjective while on the nose is an adjective.

Word	Noun	Adjective	Verb	Adverb
exactly	No	No	No	Yes
on the nose	No	Yes	No	Yes

As adverbs, exactly and on the nose are synonyms defined as:

Other synonyms of exactly include on the button, on the dot, precisely.

exactly (adjective)	on the nose (adjective)
	being precise with regard to a prescribed or specified criterion

exactly (adverb)	on the nose (adverb)
indicating exactness or preciseness	just as it should be
in a precise manner
just as it should be