The terms 'primary' and 'secondary' are very confusing in this particular situation. Transformers happily move power in either direction, what determines primary and secondary are things such as grounding and which side of the transformer gets initially energized.
When a transformer is first energized, you can see 'inrush' current as the magnetic flux establishes a balanced cycle around zero flux. Inrush is only a concern on the side that gets energized first, and gets damped by leakage inductance. Since you have 2 coils with one having higher leakage, you make the one with higher leakage your primary.
Generally voltage adjusting taps are also on the primary coils, so that you can adjust to get proper core saturation for different utility voltages.
Generally the primary of the transformer is a delta, and for grounded installations a wye secondary is preferred.
For common grid connected solar installations, the _utility_ provides the voltage reference, and the inverters adjust relative to what the utility provides in order to supply power to the grid. On top of this the transformer is generally connected to a grounded source on the utility side and is the ground reference on the solar side. This means that the utility side of the transformer is the one that is considered the primary, and the solar side is the one considered the secondary, even though power is flowing from the solar side to the utility side.
So in general for this application you will have a 208V delta primary and a 480/277V wye secondary. On the 208V side of things the utility transformer will provide the ground reference for any unbalanced current that the facility produces. If you had a wye connection, with the neutral connected, on the utility side of things you might see significant circulating currents between the two transformer neutrals as they try to 'fight' to set the neutral reference.
If you were designing a solar power system for off-grid application, where the inverters were providing the voltage reference and the 208V side of the transformer was deriving the neutral for the user, then you would need a 208/120V wye on the user side, and the 480V side would be the primary. But I doubt that is the installation you are asking about.
With that said for some installations the utility _requires_ a wye:wye transformer and uses a grounded wye in exactly the way described above as a 'no-no'. This if for something that the utility calls 'effective grounding' and is totally separate from NEC considerations for grounding. I don't understand it well myself, so if you are curious about that issue hopefully someone else will explain it.
-Jon