The erection mechanism is unable to determine the source of the forces acting on it.
It can take a guess based on the size of it.
If there's a difference then it causes a gradual correction to occur to reorient the gyro. If the turn is transient then it's correction is insignificant. Hold the turn for long enough, however...
More about size of the difference rather than duration, bearing in mind the OP was talking about electrical gyros.
If there is a big error then this is probably due to acceleration (a turn is a lateral acceleration) and therefore arrange the gyro to ignore it (by tilt switch design).
[Potential problem: What if the gyro is seriously misaligned, especially during start up? Solution: Give the pilot a manual fast erect control to override the tilt switch cutouts.]
If it is a small error then this is probably due to a gradual topple of the gyro away from the correct orientation. We can detect this and use a torque motor to make a correction.
[Potential problem: What if the aircraft undergoes a prolonged gradual acceleration, below the threshold of the tilt switch cut outs, leading to the gyro being driven into the wrong orientation? Solution: Train pilot not to make prolonged turns with small bank angles]