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:

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

On iOS:

  1. Go to Settings > General > Handoff & Suggested Apps
  2. Turn off Handoff.