A friend of mine was on that boat - you can hear her saying "uh oh" when the shark gets into the cage. This is obviously second hand information, but she was there and this is what she posted on FB.
The shark entered through the side opening (the latch to the door was apparently broken by the shark), and the diver (an instructor), rolled out of the same opening while the shark was trapped in the cage. He then waited outside until the shark got out through the open top. So he must have waited outside, hanging onto the cage breathing from a hookah wearing 40 lbs of lead on a harness! Then once the shark was out he reentered the cage and exited through the top, as you can see. Very impressive performance under pressure by that diver, but apparently no video.