If you are up to a lot of work this is possible in Blender. You will need to create a group of objects (your spheres). Each sphere will become a particle and emitted in reverse order, you can adjust the order but just be mindful that by default it is last created first emitted.
Giving each particle a particular property - in my example a different color but you might change or offset an animation. This is when you make the calculations to time everything to the particle emissions.
In my example I have 8 spheres to be emitted over 24 frames (1 every 3 frames). Maybe someone can give you a better example of how to change the color on larger sets... Offset animated color change over many objects?
I recently did this with a butterfly animation that has 1200 butterflies.
Because the flapping of the wings is looped over 10 frames I required 10 butterflies in the group offset by 1 frame. I then created 3 particles so that not all of the butterflies took off together. As I didn't want the butterflies to be flapping whilst landed I removed the cyclic animation and manually repeated the flapping from after particle launch. Prior to particle launch I slowed the flapping of some and turned the flapping off for others. I then timed and rendered the 3 particles separately giving each particles their own seed value.
But yes a magic button that can "Use Animation of object as starting life of particle" will be a nice feature.