What would cause a strong exhaust coming back into the attic from the sides of the gable-mount exhaust fan?

If the gable fan is blowing back into the attic, check to see that the gable fan is free of any debris that could prevent airflow from properly exhausting.

If it is blowing into the attic check to see that the gable fan is free of any debris that could prevent airflow from properly exhausting. Also, for Air Vent gable fans it would be best to use Air Vent's automatic shutter designed specifically for the fan.