Liftoff in the video you link is at 12:00. 13:00 on the video is one minute after the launch, not 107 seconds.
At 12:42 on the video, the "one bravo" call is heard, indicating a change in the abort mode to be used in an emergency. Abort mode IB takes effect at 42 seconds into flight, at about 3km altitude.
At 12:55 on the video, the PAO says "altitude is 2 miles" -- a little over 3 km.
So the cloud-punching is clearly occurring at 3-4km altitude.
This, on the other hand, appears to be the Phil Pollacia film. Liftoff begins about 3:45 in this video. It is ludicrously slowed down. If you compare the appearance of the rocket plume in the early seconds of flight to any other footage of a Saturn V launch, you'll easily see that it's in slow motion. The first 9.5 seconds of movement might be at the right speed, giving Aulis the reference timing that they're basing their case on, but after that it's slo-mo. If you consider the next 9.5 seconds, the vehicle seems to clear about 1.5x its own distance past the tower, for a total traveled distance of 2.5x, but according to the equations of motion, if the rocket were under constant acceleration, it should clear 4x its length in 2x the time -- and rockets generally increase their acceleration over time as they eject propellant mass, not decrease it.
According to the article, Pollacia used a Canon 1218 Super 8 camera. The timestamps in the video are obviously not contemporary; handheld film cameras of 1969 didn't have that capability. The 1218 is a multi-speed unit, capable of recording at 18fps or 24fps, with a slo-mo mode of either 45 or 53fps depending on the source. Switching from 24fps to 45fps at the 10-second mark and playing back at 24fps would match the timing pretty well ((10 sec * 24/24) + (97 sec * 24/45) = 62 sec), but the speed could also have been altered when it was transferred to video.
Aulis's next point of reference is the apparent separation of the plume, which they're claiming is the staging event. They have it at ~T+167 seconds, 55 seconds after the cloud-punching; with the 24/45 ratio I'm theorizing, it should come 30 seconds after the cloud-punching in the full speed video. That video is showing a zoomed-in view of the (distinctly unseparated) rocket at that point, but at about 13:32 it cuts to a long shot where there definitely appears to be some sort of constriction or separation in the appearance of the plume. The call here is "we're through the region of maximum dynamic pressure" also known as "max Q", which puts us at a little beyond 1:23 elapsed time. I believe the apparent plume constriction is due to atmospheric conditions, not due to separation.
Aulis is a crank site, an ongoing offense against objective truth, and a waste of everyone's time.