I'm firmly in the realms of guesswork here, so take everything I say next as "I'd probably have done it that way" rather than "that's how it is" (and by all means, please correct me!)
My hypothesis: Create as many shapes as the particle count for each particle "sublayer" - let's stick to one particle type and a particle count of 5 -- so you'll get shapes S1, S2, S3, S4, S5 - and they will stack in that order, with S1 at the bottom. Have them hidden somewhere.
When the particle system starts, display them (and move them) in sequence, S1, S2.... and that explains the initial overlap (just as you'd get in a moho vector layer with 5 shapes created in that order and each slightly displaced from one another.)
S1 now comes to the end of its journey, so it goes back to the "hidden" state. When it's time for it to reappear, it comes back - and it's still at the bottom of the stack, so looks to be under S5; then S2 comes to its end, it reappears above S1 etc etc etc...
