Once you gave the permission to access the system address book, Unibox imports all contacts on every app launch.
By default Unibox creates internal contacts for all email addresses found in your messages. In order to combine messages of people that use multiple email addresses or to rename them in the contact list, you can create a contact in the system address book and restart the app.
One email address can only be assigned to one Unibox contact, so if you have an email address in multiple contacts within your system address book it will be associated to only one contact in Unibox.
Unibox uses your address book data solely on your computer, it is not sending your data to any server. You can enable / disable address book import by changing the address book access permission for Unibox in the System Preferences under "Security > Privacy".