Distribution lists/groups are not matching.
For distribution lists, you can match with the Object with the attribute ExternalDirectoryObjectId
Follow the steps below to match both tenants
1) Run the following PowerShell against both tenants
Get-DistributionGroup | select Name,ExternalDirectoryObjectId
ExternalDirectoryObjectId ExternalDirectoryObjectId (source ExternalDirectoryObjectId) (target ExternalDirectoryObjectId)
Sample screenshot

An example of a working Groups mapping file is attached to this KB article.
Additional reference for Group Matching
How to map Groups on the Accounts tab in ODM (328103)
How to populate Group collections using a CSV import file (322919)