They didn't. The Cybermen in "The Pandorica Opens", "A Good Man Goes to War" and "Closing Time" aren't Cybus Cybermen, they don't have the Cybus logo on their chests. The Cybermen in the above stories just happen to be a similar design.
Actually, the Cybermen in "The Pandorica Opens" ARE the Cybus Cybermen - they DO have the Cybuc logo, it's clearly there. So we do know that the Cybermen from Pete's World have become a space-faring race in the Doctor's universe. So there are two possibilities for their survival.
The Cybermen in "The Next Doctor" escaped the Void but they weren't the ones that survived - they were all destroyed in Victorian London. But it is possible that other Cybermen escaped the Void as well.
Return to Earth (yes, I know the game is terrible and if you don't count it as canon then ignore this point but it has some evidence about the future of the Cybusmen. If you ignore it, they've still been established as space-faring in TPO but I just like to try and piece together the history) has the Cybus Cybermen as a space-faring race too, but they are struggling to survive, so they are likely in their early stage of space travel and gain more experience later on.
The other possibility for their survival comes from a Battles in Time magazine comic strip over four issues which feature a rebuilt Cybus Cyberman army. In the end they are defeated, but a silhouette of a Cybermen with red glowing eyes is seen, suggesting they were not all destroyed. If this is so, then it is entirely possible that they recovered and eventually developed space travel (you could even connect this to Return to Earth, doubt you will though).
So, either the Cybermen in TPO escaped the Void like those in "The Next Doctor" but to another place and time, or they are the surviving Cybermen from the Battles in Time comic. The issue may not be addressed in the television show, so I assume it's safe to choose one of these theories or even make up your own. As for the Cybermen in "A Good Man Goes to War" and "Closing Time", there is nothing which stated they were NOT the Cybus Cybermen - but nothing has stated that they are either. It's possible they changed their design too, just because the logo's gone doesn't mean they're different. But we don't know what they actually are yet. I assume it's safe to theories whether they are Cybus or Mondasian - which ever you prefer - until something sets it in stone.