The problem is then, how is the listener to determine whether something is "satire" or just a derivative composition?
When you get the reference(s) and / or simply find it funny/sardonic, etc.
A reaction like that may be due to the fact the music is -- inadvertently -- funny, but that is pretty much 'on the composer,' since listener reaction is a reaction.
(Re: 'references.' There is an inherent danger in relying on references and direct quotes; it anticipates your audience readily knowing those references.)