User fields, such as assignee can be automatically mapped in Jira and TFS / Visual Studio Team Services, provided that both Jira and TFS / VSTS server are connected to the same Active Directory instance and therefore share their user account data.
For instructions how to connect Jira to Active Directory please refer to https://confluence.atlassian.com/display/Jira/Connecting+to+an+LDAP+Directory.
To enable automatic mapping for "Assignee" field please click the "Values" link for "Assignee" mapping and select Mapping Mode "Copy Value (Attempt Type Conversion)". Please see the screenshots below for details.
To map multiple TFS / VSTS fields to one Jira field, first select a field in TFS Fields listbox or JIRA Fields listbox and then click Add selected field link (see screenshot below).
When multiple fields are mapped, it is important to be able to determine what happens during the synchronization in the opposite direction - for example, if you map fields Summary and Epic Name in Jira to Title in TFS / VSTS, what is going to happen if you have Jira → TFS / VSST synchronization enabled and there is a TFS / VSST issue to be synchronized with Epic Name field? In this scenario, the Primary field from the mapping of Jira value is used. You can select which value is set as Primary by clicking set as primary link (see screenshot below)
