After the previous meeting of Minos and Misty, the ruler of the Black Plain spent two more days in that city until he finally finished his official business there.
He signed all the necessary Soul Contracts in that period, having made official a vassal relationship between himself and the high-ranking members of the Snow family.
Because of this, that organization now had over 70% of its high-level members with a commitment to the Black Plain, something impossible to escape.
That is, of course, considering that these people would not kill themselves to free this family from the 'terrible' fate of subordination to the Black Plain.
But that would be extremely foolish to do since the deaths of these people would also benefit Minos and harm the Snow family much more significantly.