Do you sometimes skip threat result for NPCs ?

Have you expanded on table I. 6-3 ?

I don’t spend them, the players do

Like Richardbuxton said I have the players do it.

Once the players have a feeling for Threat and Advantage, and their respective limits; I tend to push much of the decision making to the table.

Many GM's run it as PCs decide how to use PC Advantages and Enemy Threats while GMs rule PC Threats and Enemy Advantages.

Yup; the rule of thumb is whoever is rolling the dice decides the positive effects, and the opposite side determines the negative effects (with GM approval). So it's the PCs who decide what happens with the NPC when the NPC rolls threat/despair, and vice versa.

Just going to reiterate what everyone else said: the active party spends advantage and the target of the check spends the threat.