If you go to your settings, then to notifications, you can set it up where you get emails when games start.
As for speed games, as long as the waiting games page is up, it pops up a notification stating the speed game started, unless you time out and it drops.
Id recommend making sure you are receiving emails from CC, and turn your email notifications on. That's probably the best way to be notified about casual games starting and it being your turn.