I've used a few carriers now and they all work differently. Verizon is the best in that they let you decide how to handle incoming calls. Whether the phone will ring forever like on an old fashion land telephone or to send it to voice mail after so many seconds. AT&T sucks in that after so many seconds the incoming call will be picked up and the caller will either get a message saying "the inbox has not been setup" and hang up on the user or send the user to inbox where they can leave a message. There is no option to tell AT&T to not interfere.
How does T-Mobile handle incoming calls? I want to replace my AT&T with T-Mobile if I can set up the phone to act like an old land line telephone. The office PBX will ring both numbers, verizon cell and at&t (or hopefully t-mobile in the future) and if I'm not answering on either number handle the call recording. So it is important to be able to set the T-Mobile phone to not pickup. Or set the pickup time for something like after the phone has been ringing for 5 minutes.