Tanks to all who replied. I do not have an option to contact the VPN administrator, as they will not tailor anything specifically for me (it is a very large company).
Yes, I am using continuity. I will accept the fact that VPN is the problem, and I will turn off bluetooth when iMac is on VPN.
Don't give up yet!
I'm actually having very similar issues as you've listed. My issue isn't with a VPN (because I'm a little ignorant and don't know what it is or how to use it). From IP checks, what I do know is that I'm not protected by a VPN.
The problem started when macOS Sierra was released. Ever since Apple pushed for better continuity, especially with iOS10 and mac OS Sierra. In one keynote event, they mentioned something about how annoying the notifications were on multiple devices when receiving phone calls or messages. I haven't been able to find which event this issue addressed specifically. I just remember a roar from the crowd.
Here's my issue: I own an iPhone 7, Apple Watch S2, MacBook 2015 12in, and iPad Air which are all running the latest software (iOS 10 and Sierra). I do not have iMessage notifications or sounds enabled on my Mac or iPad, however all devices are logged into the same iCloud and sync without a problem. For privacy I only like for my messages to come through my iPhone or Apple Watch. My iPad has no problem complying, but the MacBook takes issue. When my MacBook is logged in, nearly all iMessages notifications on my iPhone and Apple Watch fail "notify" me.
Here's what works: Disable bluetooth on my Mac.
This isn't an ideal solution. I use my Apple Watch to unlock my MacBook and at times use the instant hotspot feature on my iPhone and iPad. I've searched everywhere for the solution. Google search comes up with out-dated information, Apple.com over simplifies the issue, and Apple Support may as well think I'm someone asking their grandkid why the "email machine" won't "wif-ee".
Here's another crazy solution that seems to work.
SMS notifications broken?