Almost. The two hooks on the spring should be 90° apart. One end goes under the jack handle/tire iron, and the other goes to the jack. Does the hook on this jack come off the ratchet? If it does, it should be installed in the tire well with the jack base and the jack itself should be turned 180° to allow the longer finger of the hold down spring to go over the pin the hook mounts on.
You have 7:00-13 tires on your car ? In the spare tire well, the wheel/tire needs to go in with the inside of the wheel facing up. The long threaded bolt that slips into the floor bracket should come up through the register opening of the wheel. The jack base goes in next, upside down so that you see the bottom of the base. Then the hook goes in laying on its side with the threaded bolt going through the hole in the sides of the hook. The big threaded wing nut goes on next and you need to tighten everything FIRMLY. At this point the masonite panel goes on and what little is left of the threaded rod has the black painted metal retainer installed with the small wing nut holding the retainer and the masonite in place. The masonite will be 3/4-1" above the trunk floor. V8 cars got 7:00-13 tires as standard. It's possible that a 6:50-13 tire will be smaller enough to allow the masonite panel to sit flush. I'm betting that this basic spare tire well stamping has been carried over from the 1960-1962 cars, most of which got 6:50-13 tires.
The spring that you photo-shopped has the same hook at each end. The production spring has a larger hook with a much longer finger on the end that attaches to the jack ratchet.