Since the Asterisk phones are not recognized as internal stations, any calls coming from them are seen as Inbound External calls. The extension dialing works because your IC server is matching the DID (extension numbered dialed) against the internal extensions as part of the DNIS matching built in.
In order for the Asterisk phones to be able to place outbound calls through IC, you can do one of several things:
1) Manually create stations in the Stations container for each Asterisk phone, entering the appropriate Identification Address and Connection Address for each phone
2) Create a Remote Station station for each of those Asterisk phones, and give the people using those phones user accounts and Interaction Client. They would have to place all their calls outbound through the Client
3) Give those Asterisk users the Interaction Client and have them perform a Remote login, using the extension of the Asterisk phone as the remote number
Any of those options will require some licensing you probably don't already have, with the least expensive option being #1 (only basic Station licenses required).