Program 579 SYSTEM VOICE MAIL DATA is only used for caller ID in the voicemail system. If you are using DTMF integration, this won't work.
Program 577 assigns an extension to be a global caller ID store for a specific CO line in the system.

The program you will probabaly want is to 204 DKT paramertes - 17. This will allow a spefic number of Caller ID numbers storaged per extensions (up to system max) from 5 to 100. A zero (default) means no history

Also, unlike a VoIP system, if you had 10 phones ringing on a line, only the station that answered the call will store the caller ID. The other ringing stations will not show a missed call in their history.