Right here, but as lacking in specific knowledge as everybody else. The outer doors open inward, but the inward doors have to push outward against the pressure. Granted, the pressure at periscope depth isn't too bad, but the boat is also moving forward, so it makes sense that the tubes would be flooded before opening the doors.
Of course what I think makes sense and what really happens aren't always the same thing. Where's one of our real-life sub guys when we need him?