Seeing that there have been 1,502 views but no replies yet to your post dated June 18, 2015, I would like to try to answer your question though I'm not a native speaker of English.
Adverbs cannot be used to modify nouns as these can only be used to modify a verb, an adjective, or another adverb. In your example sentence "He did some shopping on his way home," "He" is the subject, "did" is the verb, "some shopping" is your direct object, and "on his way home" is an adverbial. The word "home" itself may be a noun but is used as an adverb as it answers the question "where?" (i.e. on his way where? home)
An attributive is an adjective or a noun that precedes a noun and describes or expresses a characteristic of the noun. (examples: new
home or capable
Therefore, in your sentence, although "home" functions as an adverb, in a sense it could also be an attributive as it describes what kind of "way" it is: a way "home." Overlapping functions may be at play here.
I don't know if the above explanation helps, if it doesn't, maybe it can serve as a springboard for further discussion of this subject.