When illaoi pulls a spirit and drops it to half health, she procs Dark Harvest on that spirit. However, she doesn't get the stack of Dark Harvest, but the rune goes on full cooldown. Moreover, when spirit is killed or vanishes, it does not count it as a takedown [while it should, since The Spirit is considered a champion, for rune and item purposes (for example Coup de Grace bonus AD, or phage item movement speed)]
1. Pick Illaoi.
2. Level up E (other abilities are optional, for damage purposes)
3. Pull a champion's spirit, and damage it to half total health.
4. Attack once more, to proc Dark Harvest.
5. Dark Harvest animation will appear, Illaoi will harvest a soul from a spirit, but it won't be counted into "Souls collected" neither will it increase Dark Harvest's damage. However, Dark Harvest will go on full 40 second cooldown.
6. After a spirit vanishes or is killed, it does not reset the Dark Harvest's cooldown, despite being a takedown.