Can an xbox360 be connected to a thunderbolt iMac to be used in target display mode
Currently, you can only use a 2010 or 2011 27" iMac with this Adapter.

iMacs build in 2009 and before doesn't support input signals. 


  iMacs build in 2010 or 2011 support input, but you have to convert the
  HDMI signal to MiniDisplayPort.


iMacs with Thunderbolt does support input, too. But there is no adapter yet to convert the signals. Thunderbolt is from Intel and they aren't very open about the drivers yet. 

EDIT: Found a german article about your problem.