The spawning of the leaves is done by animating the scale from 0 to (something).
I don’t know how the animation was actually done. I’m saying that it looks like it might have been done that way (motion sketch).
There are many ways of creating this type of animation, most of them more realistic than the example, and most of which require a plug-in of some sort to accomplish. Particular and Element 3D have been mentioned, both of which would make the particles move in 3D and could be controlled with some master controls, not requiring each individual leaf to be animated.
Even in “plain” After Effects, you could make the leaves 3D layers and make it look way more realistic.
But the leaves in the sample video are clearly not rotating in 3D. They are only moving and scaling. Which is why I was suggesting the relatively easy option of using motion sketch. The other options are more advanced: for instance, expressions could be used to create the motion of the individual leaves so that you wouldn’t have to animate each by hand. But coming up with the expressions would likely take as long or longer than animating them by hand.