They are based on your settlement population. And I just remembered that I rebalanced them, and forgot to put it in the patch notes...
There are several brackets of settlement size for the Humittes. Each bracket gives one more vizier, except for the first. Going on memory they are: 20, 40, 80, 160, 320, and 640. With another level in there somewhere, I can get the exact numbers later.
Viziers are used to operate "royal" buildings, which usually require limestone and copper/bronze to build.