When solving these problems, I tend to stick with the _same_ set of sense designations rather than switching for different problems.
I stick with the source neutral as the voltage reference, and use 'current flowing _out_ of each source terminal' as my current sense.
This view is more complex then necessary when solving for a single resistive load connected to a single phase center tapped transformer.
But I find that it makes life easier when solving for (say) multiple loads connected to a wye source. And in my research (the stuff I get paid for) I work with 'high phase order' inverters and motors where the source phase angle is not 120 degrees and changes under computer control; sticking with a single generalizable approach works much better for me than adjusting for each problem.
Carl: In the single phase center tapped system, the same current is flowing through the entire system. There is _no_ change in the current flow as it passes through the neutral point. The only thing that changes is the _description_ of the current flow.
You want to describe your voltages and your currents using the same 'sense', so that when you multiply current times voltage you get a positive number for components that supply power, and a negative number for components that consume power. (Or the reverse; the selection of positive for supply is arbitrary, but you want to pick one or the other convention and then stick with it.)
If you elect to describe all of your voltages in a loop (clockwise or counterclockwise, take your pick), then the sense that you use to describe current around the loop remains constant.
If you elect to describe all of your voltages relative to the neutral point, then the sense that you use to describe current must also be oriented with the neutral point. If (as I do) you always describe current in terms of the flow _out_ from the neutral along the various branches of the circuit, then the sign or phase of the _description_ of the current flow will flip as you go through neutral. This change in description of the current matches the description of the voltage, and maintains the convention that (voltage * current) is power supplied by that component (transformer coil, inverter half bridge, battery, etc).
This is where the 'crossing the North Pole' analogy comes into play. Imagine that you are flying from Anchorage in Alaska to Kiev in the Ukraine, on a direct flight going right over the North Pole, as you cross the pole, your path does not change; the plane does not suddenly flip around. But the description of your direction of travel changes; one moment you were headed North, and the next instant you are headed South. If you describe the path of travel in terms of 'Anchorage to Kiev', then nothing changes; if you describe your path of travel in terms of North or South, there is a flip when you pass the reference point.
-Jon