Go to the notification scheme and add a new notification, selecting "custom field" and then the name of your user picker field from the list.
@Nic Brough -Adaptavist-In this regard, I'm looking for the opposite. If I add a custom user picker, will they be notified when their name is added to the field?
It depends. The action of adding a user to a user picker could happen when an issue is created, edited or goes through a transition, so if your notification scheme says "notify users in the field when one of those three happens", then yes, they will be told.
So if there isn't any reference to the custom user picker in the notification settings, the user won't be notified?
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