A lot of people are using Twitter desktop or mobile clients which wouldn't pass a referrer. Have your direct accesses gone up?
Also, just posting links to promote your stuff is a really ineffective way to promote your stuff on Twitter. Twitter is about the conversations, not the broadcasts. Engage in some meaningful conversations related to what you're trying to promote and you'll see the benefits.
You made a good point, I saw increase in direct acesses but I need to find some ways to know that my effort spent on twitter produces that. Maybe url shortener like bit.ly can help in that regards.
Also, just posting links to promote your stuff is a really ineffective way to promote your stuff on Twitter. Twitter is about the conversations, not the broadcasts. Engage in some meaningful conversations related to what you're trying to promote and you'll see the benefits.