Custom design for Twitter button with events

You can have a custom link and still have the web intents!

The key is, instead of your link pointing to "https://twitter.com/share" it should point to "https://twitter.com/intent/tweet"

like this:

<a href="https://twitter.com/intent/tweet">Tweet</a>

This way you can use the web intents like you were trying:

twttr.events.bind('tweet', function (event) {
  // Do something there
  alert('Tweeted');
});

Check this jsFiddle