Remote Buddy only controls one application at a time and will always only trigger one action per button. The responsible code hasn't been touched for years.

What you're likely seeing is that

1) Remote Buddy receives your remote control commands through the Apple IR Receiver of your Mac - and triggers the associated action

2) EyeTV receives your remote control commands through the IR receiver built into your EyeTV hardware - and reacts accordingly as if Remote Buddy wouldn't exist.

If it is that, there are two fixes:

1) Covering the IR Receiver of your EyeTV hardware, so that it no longer receives IR signals. 
2) There's also a preference for EyeTV to ignore all Apple Remote input. You can tell EyeTV to stop reacting to Apple Remote commands by 
i) quitting EyeTV 
ii) clear the OS X settings cache by typing into Terminal.app: 
killall cfprefsd 
iii) then tell EyeTV to ignore Apple Remote commands by typing into Terminal.app: 
defaults write com.elgato.eyetv 'use apple remote' NO 
iv) launching EyeTV

You can tell EyeTV to react to Apple Remote commands again by 
i) quitting EyeTV 
ii) clear the OS X settings cache by typing into Terminal.app: 
killall cfprefsd 
iii) then tell EyeTV to ignore Apple Remote commands by typing into Terminal.app: 
defaults write com.elgato.eyetv 'use apple remote' YES 
iv) launching EyeTV

Best regards, 
Felix Schwarz