How did the World Government know about the clash between Revolutionary Army and Blackbeard Pirates?
I can think of one possible solution. The black den den mushi which can spy on people's conversations. I'm guessing that the world government (CP0 or the Marines) were either near Blackbeard or near Baltigo originally spying on either Blackbeard or Baltigo (since it is a suspicious country). Once they tapped into the conversation, they got confirmation of Dragon's location. 

The other assumption is that CP0 followed Sabo from Dressrosa to Baltigo. After following them and finding their hideout they planned a full out attack but got there to meet the place in ruins due to the Blackbeard pirates. I doubt that they followed Sabo since the Revolutionary army were secretive and careful about everything they did.