It starts after you finish all the other events in the game. Make sure you're at max romance with Ori and have mated with them at least once.
You'll find the Moki in front of your tent one morning.
As the event progresses you'll have to maintain Hazel Grove for an ingame week until the end of the event, then when the quest ends, you'll be visited by the Moki again.
To mate with the Moki, you need to call them cute at least once before the end of the questline, as they won't even think about sex until they know you find them attractive.