Does the Oracle security model support only ownership visibilty? (i.e. only records I own)

Summary:

Curious if it is possible to only allow a resource to view records they own. This also includes record results that show up in a DCL field if you start to type in it, which is currently returning all records in the system instead of the restricted access that's in already in place.

Currently, for example, as a resource in the system if I do not own John Smith as a Contact record, I cannot see that record in workspace nor can I search for it in Global Search. However, if I navigate to the Account object and select the Existing Contact DCL field and start to type the word John, ALL results in the system start to display. I need to restrict the results that show up in the DCL search list essentially.