All right, I went back and read a little closer....
If you are INTERCOMMING Ext. 10, it should be Ring and ONE Beep, not TWO (Two beeps is a transferred call)
Are you pressing Intercom and dialing 10, or are you pressing a programmed Auto-Intercom button for Ext. 10?
If you are pressing an Auto-Intercom button for 10, I'm guessing that you lift your handset, which gives you an outside line, and then press the button for Ext. 10, which initiates a TRANSFER of that outside line to Ext. 10, thus the Ring-Beep-Beep
Still doesn't explain why that call only rings once, while an outside call rings multiple times.
So you are Intercomming Ext. 10, Ext. 10 makes only one audible ring, what do you as the person calling Ext. 10 hear? Does the call continue to ring back to you while the call is still flashing at Ext. 10 after the 1st ring? Does it cover to voicemail? After how many rings.