Your AWS server's post-receive git hooks will be executed when commits are pushed to that server:
# On your development machine
git remote add aws ssh://ubuntu@54.201.12.68/home/ubuntu/
git push aws master
GitHub's web hooks work by sending an HTTP POST request to the URL that you provide when you push new commits to GitHub. If you want your site to be updated automatically when you push code to GitHub, you need one more piece: an HTTP server running on your machine that will accept the webhook payload, pull the new code from GitHub, and then redeploy. There's another question that has a bunch of possiblities you might try.