Thinking about and analyzing it further, an interval of 1/66 in interpolation essentially corresponds to a 0.015 interval on the server. So that's fine.
At 66 update rate, when you receive a new snapshot at for example, 0.04545454545 seconds, and rewind 0.0303030303 seconds back in time for interpolation, you are at 0.01515151515 seconds, which is when you received the packet for server frame 1, so you are rendering server frame 1. So when the server rewinds back to server frame 1, it matches your render position.
But now, it seems like I am missing something else, or there can be a big error on interpolation between packets, because if you shoot someone at 0.05303030302 seconds, your render time will be at 0.02272727272, it will submit a command at 0.0606060606, with tick count of 3. Then, it will rewind two frames back because of lerp ticks of 2 from 0.03030303 lerp, and then use frame 1 on the server, which was 0.01515151515 on client time. So, you see something at 0.02272727272, but the server lag compensates it as if it was on 0.01515151515. Essentially making it compensate for the base tick delay from interpolation, but not the distance interpolation introduces from the base tick values.