If someone has a penalty to a save, does is automatically lowers the matching DC?

Bon Mot for example gives a penalty to saves:

Critical Success: The target is distracted and takes a –3 status penalty to Perception and Will saves for 1 minute

If it is a critical success, and you try to Demoralize (Intimidation check against Will DC) the target, is the DC 3 lower?

If someone has a penalty to a save, does it automatically lower the matching DC?

Bon Mot for example gives a penalty to saves:

Critical Success: The target is distracted and takes a –3 status penalty to Perception and Will saves for 1 minute

If it is a critical success, and you try to Demoralize (Intimidation check against Will DC) the target, is the DC three lower?