How to disable Chrome/Safari notifications on multiple devices
This sounds like Handoff. Handoff lets you continue an action you start on one device on a different one (e.g. browsing a webpage). 

If not already, you have to disable it on every device. 

On OS X:


Go to System Preferences > General
Deselect Allow Handoff between this Mac and your iCloud devices


On iOS:


Go to Settings > General > Handoff &amp; Suggested Apps
Turn off Handoff.