You wouldn't want both the Mac and the Arduino together. If you're using a mac host, the Temperature Sensor would just connect directly to the mac and the web service runs on the mac. The Arduino replaces the mac (or Phidgets SBC) as the host, so the Mac is not necessary, and the web service runs on the Arduino.
Though I've not done it myself, it should be something along the lines of installing Linux and then the Phidget Webservice package on the Arduino. I believe that the Bonjour networking protocol needs to be installed as well, but it's possible that's installed with the web serve. Then, you should just be able to connect the Temperature Sensor to one of its USB ports. From there, the web service would broadcast what the Phidgets software running in Roastmaster needs to connect.