I have linked one question from two different websites. Provided it will get 20 visits from website A and 10 visits from website B, will I receive announcer badge?
So long as your user ID is on the end of the shortened URL and at least 5 people that visit from website B did not also visit from website A, yes you should.
The publicity badges track unique IP addresses that visit the question from one of your referral URLs. All the shortened URLs from the question and any of its answers will all count towards the same total, and you can share those URLs anywhere you want, also all counting towards the same total. So in short, it's the number of unique IP addresses that have come to that question from outside the Stack Exchange network. Where outside the network doesn't matter.