Is upside down just to show the spring lever. It is similar in arrangement to most other rattrapantes; the disengagement/isolator wheel on top, underneath is the rattrapante wheel, and finally the heartcam underneath it. Visible here:
Underneath all that stack is the usual brass chronograph wheel. This is typical of any rattrapante due to virtue of design; it can't be done backwards physically. The centremost shaft holds the rattrapante hand and wheel, then a coaxial outer shaft holds the chronograph seconds and two heartcams (one for rattrapante, the other for chronograph reset)
https://i.imgur.com/ErtsXI5.png
https://i.imgur.com/sfhywmM.png
The DS works as well as you described - able to store time mainly because it can record up to 30 minutes! Meanwhile, any other rattrapante could so the same but only for a minute long at most.
This enjoyable discussion just reminded me about a certain other novel rattrapante - none other than the AP Laptimer, which is another animal! But I digress..
Regards,
skyeriding