thanks for asking.

What you observe is not a conflict between Remote Buddy and EyeTV: 
Remote Buddy executes the actions assigned to the buttons for the 
respective Behaviour. For EyeTV, the default is "Turbo rewind" and 
"Turbo fast rewind".

However, this of course is configurable, so that if you want the 16 x 
rewind and fast forward, all you have to do is to choose the "Rewind" 
and "Fast forward" actions for the Left(held) and Right(held) entries at

Preferences >Behaviours > EyeTV

Hope that helps.

Best regards, 
Felix