For DC that is correct.
For the AC, you need to consider that in most circuits, the drift speed (actual mean velocity of electrons) is extremely slow, perhaps of order of millimetres a second. To put that in context, the alternation of an AC circuit is usually 50Hz, so 50 times a second. So the electrons on average in an AC circuit oscillate over length scales which are usually significantly shorter than the length of the overall circuit lengths. It depends on a number of factors which you haven't given, but in a circuit in your home it is easy to say that the electrons oscillating close to a wall switch will never get anywhere near the light bulb.
At this stage I might pre-empt your next question... if the electrons travel so slowly, why is electricity so efficient for transferring energy? The signal travels extremely fast, but the actual signal carriers, the electrons, are slow moving.