But seconds are 60X higher frequency than minutes. This is almost 6 octaves higher. The grid will low-pass-filter that out much better than the minute period. (You can see that trend in the diagrams given in the article: the amplitudes all get lower with decreasing period to the left, where the 60 second blip is a an outlier.)

Secondly, the amplitude drops. Events that were concentrated on the xx:xx:00 times are now distributed into xx:xx:xx times. If the overall number of events is the same, each :xx time slot now receives 1/60th of the events that were concentrated on the :00 time. If power decibels are relevant here (20 log 10 x), that's a 35 dB reduction in amplitude of the driving signal.

35 dB less amplitude, shifted to a 6 octave higher frequency that the grid doesn't react to very well can be expected to basically make the problem vanish.

This is much like the situation of soldiers avoiding rythmic marching when crossing a bridge to randomize their footstrikes.