If they didn't want the rest of the nobles of the continent finding out one way or another, they wouldn't have had the scream occur where a mere adventurer could hear it and spread the story. It wouldn't have happened at all. Everything the Zuma do is done for a reason. If a roleplay was done where an adventurer could hear it, then it wasn't meant to be secret.
but there's a difference between a secret, and something that is simply found out "naturally" as part of an on-going story.
if they wanted every single character to know about it all at once, they would have posted island-wide.