Is this a setting that is related to the IOS? I have not found how to stop it. Have you?
I have an iPhone 6 and a MacBook Air with 8.3 and 10.10.2 respectively.
iMessage for Mac has been available since 10.8, while SMS message and phone call connection was introduced with iOS 8 and OS X 10.10.
To turn off receiving phone calls, on your Mac, open the FaceTime app, and choose Preferences, then turn off "iPhone Cellular Calls".
To stop receiving SMS Messages (green bubbles) on your Mac, open the Settings app on your iPhone, go to Messages, then Text Message Forwarding, and disable your Mac.
To stop receiving iMessages (blue bubbles), open the Messages app on your Mac, choose Preferences, then Accounts, then choose your iMessage account, and uncheck the box "enable this account".
