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