If the resource manager that is identified in the sync settings has a matching email address in Autotask and Mindmatrix, any other users in Autotask who also have a user in Mindmatrix with a matching email address, will automatically retain record ownership. 

In the table below we are reviewing a contact, account and opportunity generated by the user Mark Taylor in Autotask, here we can see the record is automatically synced with Mindmatrix and owned/shared to Mark Taylor's user.  

The Contact is Brody Bronson, and the Opportunity is Edge Technology.