OS X Yosemite shares browser tabs between two different Macs, although iCloud-Safari is turned off
If you really mean by  automatically opens in task bar as a Browser icon displays a the little icon on top of it in the Dock (Handoff app icon in Dock ), and when you click it it opens the same page you are viewing on the other Mac.

then this is nothing to do with iCloud.

This a feature called Hand off. Have a read here


  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 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.