I've read in several places that the Poynting vector is directed from the primary to the secondary of a transformer (we assume here that the primary is the winding that provide the AC energy, while the secondary is just connected to some resistive load); the simulation below shows the electric, magnetic, and Poynting vector fields around a transformer.
Assuming an ideal 1:1 transformer with identical windings, both the Electric and Magnetic fields are symmetric, so there is no way to know who is the primary and the secondary from these fields. But the Poynting vector is directed from the primary to the secondary, and I found that puzzling, because I can't figure out how the Poynting vector "knows that": indeed, assuming a power factor of 1 (ideal transformer), I can make the secondary primary, passing the same current as when it was a secondary, and then the secondary (that was the primary) will have the same current as when it was the primary. So, the currents being the same, how does the Poynting vector can decide who is the primary and the secondary?

[![Electric field around a transformer](https://i.stack.imgur.com/FESPE.jpg)](https://i.stack.imgur.com/FESPE.jpg)

[![Magnetic field around a transformer](https://i.stack.imgur.com/Q9Yob.jpg)](https://i.stack.imgur.com/Q9Yob.jpg)

[![Poynting vector around a transformer](https://i.stack.imgur.com/etj09.jpg)](https://i.stack.imgur.com/etj09.jpg)