When the two demons, Rouge and Oumu, talked to each other and came to a conclusion about what they would do, they quickly moved on from where they were.
Although the air between them quickly got hostile when they confronted each other, that didn't last long since they...were friends, to begin with.
They were able to understand each other to a certain degree without even talking to each other, and Rouge definitely understood Oumu.
He knew that Oumu wanted to see Lucifer for himself, and this is because...Oumu has allowed his curiosity to take control of his decisions.
Any normal and loyal demon to the Warmester Denoble House would definitely be in outrage right now after knowing that the Patriarch of the Warmester Denoble House has been killed and now someone else is using his word to become the Temporary Patriarch of the Warmester Denoble House.
However, Oumu did not do anything like that at all.