IOS – What does it mean if the phone does half a ring before going straight to voicemail

Do Not Disturb can do that, no 3rd party app needed.

You might have to juggle a new contacts group, because it only allows to receive calls from one group at a time, or favourites - so to exclude 'work' you might need to create a new group containing 'everyone else'

You can also toggle it manually from the Lock Screen

As of watchOS 3, iOS 10, and macOS 10.12 Sierra, this is not possible, and the simultaneous rings are rather comical, if not downright annoying. What I did was:

• Disable the Ringtone in the FaceTime app on my iMac (set it to None under Preferences in OS X El Capitan, or disable Sounds for FaceTime under  → System Preferences → Notifications in macOS Sierra)
• Assign a blank Ringtone on my iPad (set this in the Settings app under Sounds—this requires creating or downloading a custom ringtone)
• Disable Sound for the Phone app on my WATCH (from the Watch app on your iPhone)

My reasoning is that the only times I'm going to pick up a call on any device other than my iPhone is when I'm already using my iMac or iPad, but not carrying my iPhone with me. In those cases, the onscreen notification is sufficient. It's very rare that I'm near my iMac/iPad and not using either of them, yet too far from my iPhone to hear it ring. Those rare cases do not seem to fall under your use case.

This is not a perfect solution, but at least it will keep you from being bothered by ringtones that keep going off while you're already answering the call. The WATCH might keep tapping you for a second, but that isn't nearly as distracting when you're trying to talk to someone.