Jack chose one week out of thoughtful consideration for his new allies. Thelgrun had much to deal with after the destruction caused by this war. They also had to chase out the retreating Liguritudum army to make sure that the enemy truly left Palgrost.
Horatio had just come into power. He also needed time to secure his hold on the empire.
As for Verremor, he had contacted Four Winds. Four Winds confirmed the alliance. Thanks to Jack's tips about the kingdom toppling quests and the information gained from interrogating the captured Raretooth and Angryfeet tribes, they managed to root out the plans before it was carried out. Two tribes were banished due to that. The Angryfeet tribe and another tribe called Toughhead.