When people say they are being "denounced" do they mean actually denounced, or just the leader popping in with a warning message?
If you trigger someone's agenda, they will pop in to tell you they are annoyed. It is possible that this confers an immediate loss to the invisible "influence pool," I can't be certain yet. However, it is different than an actual denouncement. It basically is a warning that means "a damage over time spell has been applied to your relationship with this leader." If you don't do something about it they will gradually grow more annoyed.
I think the thing that is crazy confusing unless you understand what it happening in the background is that after eating a penalty, the penalty appears to be dropping, so it feels like your relationship is getting better. But that's not true. Anytime the net total of your modifiers is a negative number, you are losing influence. So when the modifier on screen drops from -16 to -5 and you're thinking well they should probably be okay with me now, they actually aren't. They're still losing influence, a bit slower than before, but still on the next turn they will like you even less. It's all very confusing because the way the relationship screen is designed, the numbers look exactly like in Civ 4, where you could just add them up to determine your current relationship, but here that total seems to represent the per turn change.