The term determiner is newish (about 80 years old), and hasn't had much uptake in school grammars. The study, in English, of French and other modern languages has employed the term DETERMINATIVE ADJECTIVE since at least 1806, when Dufief wrote,
"S. Why do you call them determinative?
M. Because, when they are expressed before nouns, we know how often the object represented by the noun is repeated" (p. 40).
In 1924, Palmer was the first to try to corral this group of theretofore-heterogeneous English words by adopting the concept from the French analysis.
"To group with the pronouns all determinative adjectives (eg
article-like, demonstratives, possessives, numerals, etc.), shortening
the term to determinatives (the "déterminatifs" of the French
grammarians) firstly because there are divergent opinions as to
whether they are adjectives or pronouns, and secondly, because most of
the members of this category may be used indifferently as pronouns or
as modifiers of nouns" (p 24).
And, in 1933, Bloomfield introduced the slightly different term, DETERMINER, into English linguistics when he wrote,
"our limiting adjectives fall into two sub-classes of determiners and
numeratives [1]... The determiners are defined by the fact that
certain types of noun expressions (such as house or big house) are
always accompanied by a determiner (as, this house, a big house)" (p
203).
Technically, "warm" modifies "cup." But it's interesting to note that English does have the concept of a compound noun. This means that "tea cup" can be considered a compound noun and, therefore, "warm" modifies "tea cup." The same would be true for "mean person," but it's usually easier to simply separate all the adjectives and nouns.
This becomes more obvious using the example, "cup of tea." Due to the function word "of," "tea" is the adjective modifying "cup." The third definition of "of" from Merriam-Webster states:
["of" is] used as a function word to indicate the component material, parts, or elements or the contents • throne of gold • cup of water
Thus, "warm" is still modifying "cup" in the phrase "a warm cup of tea."
Best Answer
Grammatically, "well-known" qualifies "writer". You can tell this since they are placed in juxtaposition in the order adjective->noun, the usual method in English.
Semantically, "well-known" might be understood to qualify both to some extent, since the copula "is" equates the two. However, consider that:
does not mean the same thing. Your sentence means "among writers, Ruskin Bond is well known." My sentence means "Ruskin Bond is well known, and happens to be a writer."