Perhaps I understand what are you troubled about. You are right that a changing magnetic field induces in a coil a flux of electrons.
As long as the coil has open ends the amount of fre electrons is small and this amount will be moved to the one end of the coil and the inductance process stops. After the magnetic flux changes its direction the same amount of free available electrons will be moved to the opposite direction.
If the circuit isclosed a max bigger amount of free electrons is availible from the closed circuit and the electrons allong all wires will be moved nearly at the same time. This is because the change in electric potential in the generator changes along the wire with the speed of light (or at last very fast) and all the free electrons moving at once (but the drift velocity is comparing to the signal velocity very slow).
To say it short, a changing magnetic flux induces in a coil the movement of all the free electrons along of the circuit with a signal velocity of approx. the velocity of light. So every change in magnetic flux at once moves all the free electrons in the circuit and this with the frequency of 50 or 60 Hz.