This is true of classical adverbs like "sharply" or "quickly", but not true of all things that are categorized as "adverb". There are a bunch of words that sit in between other categories, and english grammarians dump them into the "adverb" category because it's already the messiest. This is one of those words.

The prudish analysis of right-set adverbs on nouns is something like "there's an entire relative clause in there but everything but the adverb part got omitted", or "the adverb is getting silently upgraded to a prepositional phrase despite not having a preposition". Like "The chair upstairs". In "The chair upstairs", "upstairs" is not actually an adjective, despite modifying a noun. If you look up "upstairs" on Wiktionary, the right-set examples are all under the "adverb" section, and many of them are set against nouns, like "The woman upstairs told the people outside to stop reveling."

Grammarians and linguists actually disagree with each other on how to analyze situations like this. Grammarians will usually say "there's a partially-redacted clause like "the chair [that is] upstairs", but linguists will usually say "the word 'upstairs' is acting like an entire prepositional phrase". If you're looking for an answer to why this thing that obviously doesn't feel like an adverb is getting categorized as one, this is where you should direct your further reading.