By default, a Salesforce lead, contact, account, or opportunity record will sync its Owner field to the HubSpot Owner property on the corresponding HubSpot Contact, Company, or Deal. Please note that any Salesforce owner will sync to HubSpot as an option for the Owner Field, but only HubSpot Owners that match an active Salesforce user's name and email will sync. (If HubSpot attempts to set an Owner value that doesn't exist in Salesforce, the Owner value will be reset to the last value from Salesforce.) After the initial sync, changes using matching owner information will sync from either Salesforce or HubSpot.
Salesforce Lead Assignment Rules will apply to new Salesforce leads created by HubSpot, unless the HubSpot contact is assigned a valid Salesforce Owner before the record's first sync. An owner is considered valid if its name and email match in both HubSpot and Salesforce. After the initial assignment in Salesforce, changes to the owner field in either HubSpot or Salesforce will sync to the other. Read more here about how lead owners get assigned.