Total Mix is not set up like a typical analog board, which is what you drew above. It helps to think of it differently. On an analog board you have a primary signal path to the Mains (the green lines in your drawing) with some number off aux sends splitting of at some point. It helps to think of TM as a series of an aux send with no "primary" signal path. So, each output is mixed in the exact same way and completely separate from each other. The only exception is the internal effects sends, but let's ignore that for now.
In your specific case - first make sure your routing is set to "submix". This should be the default but check to make sure (upper right part of the TM window). Now, click on the third row on the "phones 3" output (this assumes you have assigned it correctly already). You will see this output highlighted so you know it is selected. From here, every fader movement in rows 1 and 2 (inputs and playbacks) will affect only the Phones 3 mix. Once this mix is correct, click on the third row "Mains" output and you will see the faders on rows 1 and 2 jump to reflect this particular mix.
All of this is covered in the manual, and the links Daniel sent provide a good introduction.