Does increased chill effect increase the minimum of "Chills always reduce by at least x%" effects?

If I have for example the Cold Mastery passive that makes my chills always reduces an enemy's action by at least 10%, would having 40% increased chill effect make it always reduce an enemy's action by at least 14% even if I hit it with just 10 cold damage?

Or would it still only be 10% and getting more than that even with Increased Chill effect would require me to hit it harder?