In this instance, one fix is to fire the timer every 59.XXX seconds, so it will naturally drift out of phase with the minute hand of the clock.
If work needs to be done exactly every 60 seconds, this is fixed by having a WAIT(RAND(60e6)) microseconds during the first timer initialization, so if 10,000 units start simultaneously they don't try all at once. This is good practice in most (all?) systems. Hint: test power and infra outage/reconnect, which can unintentionally sync timers.
This is why many software will do automated updates every 17 hours: 17 is coprime with 24.
Classic "thundering herd" mitigation tactics.
Edit: Tempting to blame IoT, but (since this is news) I don't think anyone knew there was something to fix here. We have the tools however.
It's sort of a solved problem - the ones I'm aware of are things like LynTec sequenced panels built exactly for this, and Siemens' SENTRON semiconductor CBs where you can control then curve to your spec.
Convincing stakeholders though, is almost a job of its own.
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.
You want your jitter to be significantly >> than the time your task takes as otherwise you get non intuitive degradation that can reintroduce the problem you’re trying to solve. It’s a balancing act picking the jitter that drops off the thundering herd enough and one that is still greater than the time your work takes.
But yeah, as soon as you start using Rand most people make all sorts of mistakes. And if you’re using C Rand, don’t. It has other statistical problems.