I have two Macs on the same Apple ID. Sharing issue When I access the internet on Mac 1, the other Mac (Mac 2) has a extra icon pop up and can see what I access. Both Macs use the same Apple ID and are on the same domain. Two different users are signed on. 

For instance, I will go to espn on Mac 1. The person on Mac 2 will have an extra Safari icon pop up. That person could click the icon and see what I am seeing.

How do I stop this?
This is called hand off

It allows you to continue where you left off in an app on one Device when you are accessing another device.

It works via the AppleID not the local user.


  When your Mac computers and iOS devices are within Bluetooth range of
  each other (about 33 feet or 10 meters), they can automatically “hand
  off” what you’re doing from one device to another. For example, you
  can start writing an email in Mail on your iPhone, then instantly pick
  up where you left off in Mail on your Mac.
  
  Handoff app icon in Dock Handoff works with several apps that come
  with OS X Yosemite and iOS 8: Calendar, Contacts, Mail, Maps,
  Messages, Notes, Phone (iOS only), Reminders, and Safari. It also
  works with Keynote v6.5, Numbers v3.5, and Pages v5.5 for Mac, and
  Keynote, Numbers, and Pages v2.5 for iOS. Third-party apps may also
  work with Handoff.




You can turn it off under the General Preference Pane in System Preferences