Import2 does set the owner for all records during the import. However, it is a limitation of HubSpot that the record owner is not displayed in your timeline view for the Engagements. Instead, HubSpot uses the "created by", which is set during the import by HubSpot and cannot be edited. This is different than if you create an Engagement record manually. See here for more detail.
For your Contacts, Companies and Deals, you should see the "Owner" field reflected correctly as long as: