I don't think it's possible for 3rd party QuickTime capable apps to talk to a TV tuner like the EyeTV 250 without what is known as a specially-written
VDIG - Video Digitizer QuickTime component. In the early days of Mac video capture, way back to the 1990's and the VideoSpigot era -- a VDIG was the software bridge between video hardware and QuickTime capture apps.
A VDIG would allow you to take, say, a Mac TV tuner's signal and transmit it someone in an iChat session, and would be a selectable source just as an iSight or external USB webcam might be for any number of applications. I remember emailing ElGato's support years ago asking if writing a VDIG for EyeTV was in the cards. It never came to be...
Doc -
http://www.mac-digital-tv-tuners.com/