sparkee,
The diagram that you've just presented is _not_ a 120/208V system, but is instead a 120/240V _single_ phase system. If you redraw the diagram with 208V between legs rather than 240V, then the diagram will be wrong.
In the 120/208V system, you have to have at least two transformer cores, each on a separate phase, supplying a separate supply leg to the residence. The two transformer 'legs' carry magnetic flux 120 degrees out of phase, generating voltages that are 120 degrees out of phase. The vector difference of 120V at 0 degrees with 120V at 120 degrees gives the 208V.
In the diagram that you've presented, you only have a _single_ transformer core, so both coils must be in phase.
-Jon