Is my apple ID compromised after receiving notification of Facetime from unknown computer?
That alert will popup every time someone link your Apple ID to a new device. 

Short answer: if it's not your Mac, yes your account is compromised. 

When you try to activate FaceTime or other Apple service on devices you have to log in using you Apple ID and password. So basically someone just entered this info. 

First thing to do is to change your password, secret question and answer. Now double check your recovery email address and password associated to it. 

After that every devices log off and prompt for the new Apple ID credentials. 
Now your account is safe.