semiotics
/ˌsiːmɪˈɒtɪks,ˌsɛmɪˈɒtɪks/
noun
the study of signs and symbols and their use or interpretation.

Is there a general philosophical concept that successfully describes why symbolic things have emotional meaning to an audience as opposed to the creator? — TheVeryIdea

Art criticism might have something to say about that.

Symbols are generally located within a cultural context and vary across cultures.

In the Western tradition in art Hall's Dictionary of Subjects and Symbols in Art will shed light on traditions long forgotten by most.

roland barthes, in particular: "image, music text" could be helpful,

semiotics combined with psychoanalysis, would be the way i would approach the question, if you wanna be more critical then maybe add modern marxist thought to the mix.

psychological/biological theories tend to be more reductive,

those things within an art work that draw us in and with which we make an emotional connection. — TheVeryIdea

On seeing Munch's Scream, the screaming face has an immediate emotional meaning.

But the screaming face also has a symbolic meaning, a symbol of of despair, which, when one reflects on it, may result in the remembrance of an emotion of despair.

The question is, when I look at The Scream, am I looking at an analogical representation having immediate emotional meaning or a symbolic representation having a cerebral symbolic meaning which may subsequently result in an emotional meaning.

Is there a general philosophical concept that successfully describes why symbolic things have emotional meaning to an audience as opposed to the creator? — TheVeryIdea

Emotions do not have meanings.
A meaning basically signifies what is meant by words, ideas or actions.
A meaning is an implied or explicit significance or an important or worthwhile quality, a purpose.
Nothing of any of the above can be applied to emotions.

Emotions have impacts.
We do not create emotions. Emotions occur. They are the effect of thoughts, which may be created consciously or unconsciously (from the subconscious).

Symbolic things may have an emotional impact on some people and not on others. A painting showing a mother holding her baby in her arms can symbolize affection, and it may produce an emotion to some persons but not to other. The creator of the painting might had no emotion whatsoever in the conception of the subject and during painting. His emotional involvement or absence of emotion regarding that painting is totally independent from the effect it may have on others.

The emotional effect symbolic things have on a person depends on his personality, his memories, his experiences, in short, his whole life. But since the lives of people have a lot in common, i.e. people having common experiences, some symbolic things may produce common effects to a lot of people. Example: A gun, a kiss, a flower, a color, and so on.