Alex didn't give any warning to the big powers because he knew when they knew he was uncomfortable with something, they would definitely do it, and its end would be a war without an end where, even with the restrictions, he would find ways to make them suffer immense losses.
Alex didn't want to start a war that would have no end because he had other important things to focus on, and dealing with tens of power-hungry basterds was not one of them.
The following week went without much of an issue, as the organization lost close to three hundred players in total, with only a tenth of them belonging to the Twilight Embers school.
Alex also personally talked to the school elders on their stand because he was worried about their safety as he didn't care if the organization lost 90% of the members, knowing they were replaceable, but he didn't want any blood to be spilled, which could be easily avoided.