Unless it is DC. The DC component of the secondary current adds a DC component to the core magnetization, but is not reflected by any primary current to cancel its effect on core magnetization.
Try putting a resistor or an incandescent lamp in series with a diode, with a jumper across the diode, and power that with a transformer. Put a resistor in series with the primary so that primary current can be shown on an oscilloscope. Watch what happens when you unshort that diode.
Magnetization is caused by difference between primary amp-turns and secondary amp-turns, times core permeability. Volts per turn is proportional to time derivative of this times core cross section area.
A DC component of current in either winding will add magnetization to the core without causing any induced voltage.
- Don Klipstein ( snipped-for-privacy@misty.com)