They don't have to be loyal to him even after death, per say. They just have to believe in the cause and want it. The individuals that are close to him believe in Jack's visions, people who he shares the same goals with. 

That's the reason his soldiers are trained to give their life for the country and not Jack, so him dying doesn't hinder any advancement of plans.

Loyalty in people? They get better payment than they did with the previous kings, the families of course. Even if the man are working nonstop in the mines and whatnot  their families fare better.

And aside from this, don't forget the religion that has also been heavily influenced by Jack himself. He controls the religious organ, the church. That means the people, as the church pretends to be on their side and the people support it likewise.

And what about his secret police? They have directives, they won't let things go array and they would make sure that things went according to him in case of his death.