The transformer is for control voltage only. The 120V power it supplies operates the coils in the contactors, panel lights, etc. The control transformer only supplies roughly 150 watts of power at 120V.
The heating elements on most multi-voltage ovens are wired in series for 440V, doubling their resistance. By re-wiring the heating elements in parallel, you effectively half the resistance. Thus, the oven will then produce just as much heat at 220V as it did at 440V. The oven likely has provisions to do this in the form of terminal blocks, shorting bars, etc.
The control may or may not have provisions to wire the unit for 208V. They may simply allow the 220V connection to suffice, with a slightly lower maximum operating temperature being the only consequence.
NOTE: I have seen dual-voltage machines where the main service wires within the control were too small to support the lower voltage connections. Remember that with power being constant and voltage dropping by half, current must double. I would be certain to contact the manufacturer before proceeding. Even then, double-check the incoming wire sizes to be safe.