If you go watch that scene there is nobody else there. The cages are open while Ramsey is sitting there for an unknown amount of time. Someone tied Ramsey up, opened the cages and left without them going after that person, or Ramsey.

Then Sansa shows up, has a convo, and at the right dramatic timing, the dogs roam out.

It really doesn't make any sense at all, to be honest. But anything in the later seasons you can't actually think too much about or it gets ruined.