1. User which is being assigned the story in Agile 2.0, there should be the same user(with exact same email id) in Jira system as well. We are mapping for the exact email in the Jira and Agile 2.0 side, Once the email matches in both the sides that corresponding user is set in the 'Assigned to'(assigned_to) field or any custom fields.

2. Some custom fields aren't populating from Jira to Agile 2.0 because email visibility was restricted to 'only you and admin'. That should also be changed to 'ANYONE'.

Follow these steps in Jira instance to make this change.

Go to profile and settings -> Manage account -> Contact