'Good' is a somewhat tricky word to use as an example, as it can be used as an adjective or adverb. It is probably more common as an adjective ('I am [a] good [person]'), but it is also increasingly used informally as an adverb to replace words like 'well' or 'fine' ("I'm good, thanks" invariably is used to mean 'I'm fine').
Anyway - assuming you mean "I am good" as an adjective, and the sentence means "I am a good person", then "good" modifies "I". Who is good? I am.
According to the Grammar handbook you link to, 'on the northeast tip of Illinois' is an adverb phrase, based on their logic that adjective phrases always immediately follow the noun they modify. Adverb phrases, in contrast, follow the verb.
You are asking, in effect, how 'good' can be an adjective when it follows a verb, when that would be considered an adverb in a prepositional phrase. The reason is, "good" is not a prepositional phrase. It is simply an adjective. It is the preposition in the prepositional phrase which changes the 'rules', so to speak.
I'm not even sure the distinctions being drawn by the 'Writers Workshop' page are very useful. Consider:
Chicago is on the northeast tip of Illinois.
Chicago is a city on the northeast tip of Illinois.
The first, we are told, is an adverb phrase. The second is an adjective phrase. I'm happy to be enlightened by those that know better than I do about the usefulness of this distinction, but my initial reaction is 'so what?' The sentences are to all intents and purposes completely identical in meaning. In both cases, as @Mixolydian says, it is Chicago, the city, which is in effect being described, regardless of the precise grammatical distinctions.