While the Hauppage HVR-950 stick for Mac doesn't come with an IR remote control, the Windows product based on the same hardware does - as indicated by this chart at Amazon.com: 
http://ecx.images-amazon.com/images/I/519-4YvO2QL.jpg

It's therefore highly likely that this product contains an IR receiver of its own and is leading to the phenomen you describe. This is something you can try to find out:

1) Play back a recording in EyeTV and control its playback with your Apple Remote via Remote Buddy. Does the problem occur? 
2) Unplug the TV stick. Now repeat step 1). Does the problem occur as well?

The Mac's IR Receiver can only be accessed by one software at a time. Since Remote Buddy can only react to the Apple Remote when it has access to it (and thereby automatically excludes EyeTV from accessing it at the same time), I can't think of any way other than a separate IR receiver in the EyeTV hardware (or Hauppage hardware in your case) whereby EyeTV could receive your button presses and react to them at the same time.

Best regards, 
Felix Schwarz