I think "soberano", applied to an audience, means this: they're the boss. The audience is king. You can actually say the audience is sovereign. Look at all these results:
https://www.google.es/search?num=100&q="audience is king"&oq...
https://www.google.es/search?num=100&q="audience is sovereig...

I wouldn't use those here, though "they're king" is a possibility. But rather than independent (not influenced by the views of others), I think the idea is that that they hold and exercise supreme power.

I would be rather inclined to say "they call the tune", as in the saying "he who pays the piper calls the tune", as it is a set phrase with the right meaning but also carries an element of wordplay: if the audience doesn't like a tune, they don't play/sing it.

Here's a reference which points towards the meaning I'm suggesting:

"El público soberano
No debería asombrarnos que el público mande. Ha ocurrido siempre aunque no con la rapidez y el alcance de la actualidad. Primero fueron los emperadores en el circo. Los espectadores, con sus aplausos y gritos, salvaban la vida de los gladiadores [...]"
http://lector.kioskoymas.com/epaper/viewer.aspx