Incoming calls arrive from the provider and are routed by the number that was dialed.
Incoming calls now reach the right phone, chosen by the number the caller dialed.
Routing by the number called
An office usually has more than one number: the main line, a direct line or two, maybe one printed on an old sign nobody wants to change. Each number can now lead somewhere of its own. A number with no instructions rings one extension you choose as the catch-all.
Providers do not agree on how to write a phone number. Some put a plus in front, some do not, some leave off the country code. So Pidgin Talk compares digits only, and a number matches however it was written down.
Is this really the provider?
A call from a provider does not sign in the way a desk phone does, so the system has to decide whether to believe it. It does if the call comes from one of the provider's own server addresses, which it learns from the provider's name.
Anything else is treated as a desk phone and must prove who it is.
One rule we will not bend
A call that arrives from a provider is never run through the outgoing dialing rules. Not for any reason.
If it were, a stranger could call your main line and, with the right digits, dial straight back out through your account. Phone fraud of exactly that kind is old and expensive. Keeping the two paths apart shuts the door completely.
Where we are
Calls in, calls out, calls between desks. That is a phone system, of a kind. Now to find out what breaks it.