As Mike said, Your not using the Tascam ASIO drivers.
First disable the realtech, get that bastard out of there or you'll have these kind of issues. Go to devise manager. You can always enable it but you don't need it anymore. Choose share drivers with other programs.
If that still doesn't work then you might have installed the wrong set of drivers, double check if your system is 32 or 64 bit. Get them from here. Don't use the disk.
http://tascam.com/product/us-600/downloads/ It looks like you have installed the Tascam drivers or you wouldn't get the control panel. It looks like it is set properly.
Thanks for the screen shot, that totally explains everything clearly, wished more would do that.