At Oswald's words, the people in that hall debated for a few seconds until they agreed to temporarily accept Minos as that man's successor.
The sect master had said he would be in charge of everything crucial for the sect in the short term. On the other hand, Minos would prove himself on the battlefield before he got any benefits. So they were willing to accept it since, as much as Oswald gave them this chance, he could appoint his successor without consulting these people.
In the Gray Clouds Sect, there was a custom for the sect master's successor to go through a series of tests and be approved by the council of high-level elders. That had been followed faithfully by the leaders of this organization since ancient times, something that had long since become a custom in this place.
But there was no obligation for the current sect master to do this, and these people knew that Oswald could impose his will if he wanted to.