The Conflicts database is maintained separately from the Contacts database. In order to add a Contact as a Conflicts record you will need to click on the Conflict Search Button, click on NEW and add it.
You may also add Conflicts records through clicking on the Client record or the Matter record and then clicking on Action > Add Conflict Record. This allows you to add a new Contact directly into the Conflicts database and will automatically associate it with the Client record or Matter record for you.
The other place Conflicts records may be created is on the Matter Intake Form under the related parties section. These records will be added to the Conflicts database when the Form is completed and a Number is assigned.