My idea was that the ion pod is similar to a travel pod. The Enterprise's mission was to do surveys of ion storms and was carrying several ion pods on the flight deck. The pod was docked to a docking port on the side of the secondary hull. The pod carries new, special instruments and sensors that the Enterprise doesn't possess. In order for the sensor to work to full effect the Enterprise had to have her shields down when she entered the storm. If the shields conform to the shape of hull of the ship, the pod protruding out the side would prevent the shield from being fully raised, so the pod would have to be jettisoned to raise the shields. The diagram seems to show the dock being just off the shuttle maintenance shop, my idea was that the docking port was in the same position as in TMP on the side of the secondary hull, but usually covered with an armored hatch.
The Enterprise was in an area of space known for intense ion storms, perhaps diving into stronger storms each time. Much like the Air Force flying into hurricanes. Finney did manipulate the duty roster to his own needs, he avoided the first pod duty because he needed a record of Kirk pushing the button on a pod jettison. When he was ready he placed his name at the top of the duty roster, probably altered any sensor logs showing the docking port hatch to show himself still in the pod when the hatchs closes prior to jettison.
I still can't work out how Finney would eventual ever get off the ship.