Hello,
I didn't have any problems having the HDHomeRun working with EyeTV.
I am using EyeTV 4 version
When you start using EyeTV, the assistant asks you to select your country (France in my case), and then it asks you to select your hardware.
In this case, you have to select the Manufacturer (Geniatech), and then the Product (HDHomeRun, at the bottom of the list).
Then you are to enter your license activation key,
Then you are supposed to connect your DVB-T antenna to your HDHomeRun and then your HDHomeRun device to your computer or your router with the Ethernet cable. Et voila!
Hope this helps, let me know if any more questions,
Eric