I’m thinking of the placement of the Latin phrase, ad hominem as it is used in English, not as it is used in Latin. Should it precede or follow its noun?
Before the noun; after the verb.
The bolded part is your clue. Postpositioning treats it like the prepositional phrase that it is in Latin.
In English, ad hominem is treated that way as an adverb ("argue ad hominem"; "designed ad hominem") where it's distinguished from ad rem and hews closer to its Latin meaning of "to/against the person".
It still means "concerning the persons of one's opponents rather than the substance of their arguments" as an adjective but it's been nativized and grammatically functions like a more exact form of "personal": "ad hominem attack"; "ad hominem appeal"; &c. Every one of the OED's usage examples follows those patterns for the adv. and adj. senses.
You can treat the Latin phrase as a Latin phrase and place it in English as though it meant "to the person". You're just expecting your audience to parse it that way and most won't. They just know it describes a certain kind of effective but illegitimate argument and/or rhetorical fallacy.