Twitter has released an update to their official Mac app today. it includes support for Notification Center, fixes for Growl and more.
Notifications can be configured in the Settings, and, in my initial tests, they worked fine for mentions and direct messages.
What’s New in Version 2.2.1
Notification Center integration: receive notifications when someone mentions you or when you receive a Direct Message. You can configure this from the app’s Preferences window.
This update also includes the following changes:
Twitter for Mac is available FREE in the Mac App Store. [DIRECT LINK]