I have two Macs on the same Apple ID. Sharing issue

Solution 1:

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