Can confirm this, and your explanation is sound.
Your interpretation of normal go rules is interesting to me - the idea that captures are resolved first and then the stone is placed.
I’ve always thought of it in this order - first stone placement, then resolve captures of opponents stones, then check for self capture.
Yes, you can think of it as three steps:
1.) stones are placed at the same time
2.) old chains without liberties are removed
3.) new chains without liberties are removed
… where chains are called “new” if they contain a stone placed this round, otherwise “old”.
So if the stone placed at D5 was only white-green, then the capture would have occurred as you expect.
We can take black-greens capture at D9 as another example. After placing the stone, the black chain has no liberties, but since E9 is an old chain that gets removed in step 2., D9 survives.
This is where it works intuitively, in my opinion. Needless to say, there are many unintuitive examples as well 
I believe the whole idea goes back to Diplomatic Go
Note that this mechanism is compatible with normal go rules - here all opponents chains are “old”, and self capture can only occur for the chain containing the newly placed stone, i.e. a “new” chain.