Why does an inbound call not create a contact automatically, and when is a contact created?

Calls do not create a contact automatically, otherwise your CRM would fill up with bare phone numbers.

A contact is created during the call, not when it ends, by the steps you put in the agent's workflow:

1. Use the Contact Lookup step to check whether a contact already exists with that phone number. If there is no match, it creates a new contact with the fields you specify.
2. If the agent asks callers questions such as name, email and phone, use the Ask and Save step so the answers are saved to the contact.

When the call ends, the Call Ended run takes the call transcript, extracts its dynamic variables and attaches them to the matching contact if one exists. You can see each run, the matched contact and the extracted variables on the agent's Runs page.