Yang Yi no longer needed Justin to fulfill his third condition; he only needed Justin to help him spread the two messages.
As Justin said, the Cicero Family had to be responsible for the messages they put out, so the Cicero Family was essentially endorsing the Organization of Water.
Once Yang Yi's first message was released, whether or not the Organization of Water truly was the best, it would be from now on, because this was acknowledged by the Cicero Family and endorsed by Cicero.
When the Cicero Family started advertising for others, who knows how many collaborators would be angry about it, but Justin owed Yang Yi and the Organization of Water a huge favor.
A favor must be repaid, so even if Justin had to break new ground for the Cicero Family, he had to meet Yang Yi's conditions.