I haven't tested it extensively, but I believe it starts after the first upgrade to the farm. So, the initial purchase works, but the second you upgrade it the milkers bug out. It's been a minute since I've been there though, so it might have just done it at the start. All I can say for sure is that it does do happen and it's anytime there are people (Cows) in the milker. The hatchery works fine, other than the nurseries all getting reup up with your Head Girl instead of your Farm Manager. XD