When you start or complete a DLC, it normally posts on your feed that you did.
On my profile on Feb. 4th, I have "Ulkesh started the Enter The Dominatrix DLC for Saints Row IV". But when I completed that DLC on Feb. 13th, it didn't post a message. And when I started the next DLC for the same game, "How the Saints Save Christmas", on Feb. 14th it didn't post anything either.
Oddly enough, I can enter a completion time for "Enter The Dominatrix" so it did register somewhere that I completed it, but it didn't post on my feed and didn't send me a PM about the completion either.
Ulkesh