Call Handling Set up

Why would the phones be answered the second time when no one answered them the first time?

I agree with your first two steps being pretty typical, but Stephen makes a good point that it is likely no one would be available just a few seconds after they were not available the first time.  This also would create a loop and callers would just repeat through the process endlessly until someone answers or they hang up.  This is sometimes referred to as "voicemail jail" :)
I would consider using a call group to hold calls in queue with announcements and music or letting calls go to a mailbox after some period of time.