In this case, the adverb/adjective pair "seldom upset" acts as an adjective to describe "one." The phrase has an implied "that is," as in "one (that is) seldom upset."
This is very formal phrasing, almost never used in conversation and rare even in print. When you do see the "one [adverb] [adjective]" construction, it is most common for the word "so" to be used as the adverb.
"It is rare to see such skill in one so young."
"I've never seen one so big!"
Adding to the confusion in your Flowers in the attic example is the fact that "one" can be a noun or an adjective, "seldom" can be an adverb or an adjective, and "upset" can be an adjective, noun, or verb. Out of context, "one seldom upset" could mean:
- A single surprising outcome that is infrequent (adjective / adjective / noun)
- An individual disturbed someone or something infrequently (noun / adverb / verb)
- Something or someone that is rarely disturbed (noun / adverb / adjective)
The only way to understand its meaning is through context. In this case, the key is to recognize that "one" is the indirect object of the sentence, not "upset."
If I were to rewrite the sentence for clarity, I might substitute:
"Such a vehement outburst from one so rarely upset..."