Unless the Shadow Complex really doesn't work with people, like they don't even use money and just steal everything, simply interacting with others adds a chance that someone could discover them. Think of it like the Batcave; did Bruce Wayne hire people to make it or did he do it all himself? Some people have been caught merely because of a dollar they've used. Not usually possible, but than again, an organization who's very existence is unknown to the world, despite perhaps doing some of the most controversial thing? Odds are about to same. Plus, there is people who know who the Shadow Complex are. The Teen Titans. Do they know they exist or even anything about them? No. But that's where Dark Matter comes in.

Being one of the more notorious, if small time, criminals lords, Dark Matter's reputation will be catapulted into public enemy if the Shadow Complex really wants to get him out of the way. So he'll work with the Teen Titans. This will allow him to discover the Shadow Complex through John, who believes that Jack works for them due to his past meeting. While the Teen Titan's can't exactly help Dark Matter directly due to the fact that he is very much a Criminal, he will embrace his new found infamy. Namely, by doing what Dominick planned to do with that warehouse; take it for himself. He will create the Shadow Complex, and use it to stage attacks of terror across the world. This will spread the name of the Shadow Complex everywhere, and in doing so, they will attempt to find out about this Shadow Complex.

In doing so, we create something of a Schrodinger Cat; through Jack you claim that the Shadow Complex does not exist. Though Dark Matter I will claim that it does. By working with the Titan's to stage these events, and eventually rising into the ranks of the Justice League in order to gain their involvement, Dark Matter would raise the awareness of the Shadow Complex through independent as well as the resources provided by those allied with the Teen Titan's. 

Of course, this plan has a lot of moving parts and things could go wrong. Often they do. The main thing we have to figure out is if Dark Matter get's framed. And, of course, if the Teen Titan's are willing to be so underhanded as to allow criminal acts to occur simply to lure out the Shadow Complex or raise the awareness of their existence. It also depends on what John knows.