On jira cloud, I have added a custom field to several issue types. The type of the field is a single user - so I can select from a list of users (same field type as the assignee field uses).
When anyone chooses a user for the field it does not notify the person who has been selected.
Example
New Field on Bug report
Name : Test Team Member
Type : Select Single User
- I create a new bug
- enter a team member call "Dave" in the Test Team Member field
- Dave does not receive any email notification telling him that he has been applied to the Jira Bug
Obviously the notification works if Dave is made the assignee etc on the bug, but not for any custom fields.