These types of older slave clock systems used to be very common in schools in the US (they are still sometimes installed in new schools but usually using newer digital schemes integrated with the paging system). Factories and other campuses also used them but I have not seen this so much personally.

A very common control protocol, used more or less by IBM, Simplex, and Standard Electric, is this: a pulse delivered once per minute advances the minute hand one notch. A pulse delivered at the top of every hour (on a separate wire, I believe in the Simplex case that I am most familiar with) powers an electromagnet which "snaps" the minute hand to the 00 position, correcting any error that occurred in tracking the minute pulses over the preceding hour.

If the clock is doing a poor job of tracking the minute pulse (due to a dirty/bound up local mechanism in the case of school clocks I've messed with), it's common to see the minute hand perhaps ten minutes behind late in the hour, and then at the top of the hour it will fairly quickly "sweep" to the correct position. Of course these clocks should be serviced, but the school district I was dealing with had a paltry budget and a hard time finding companies to service the clocks so they tended to stay broken in this way for years at a time.

The big problem with this system is that it could only "correct" clocks that were a bit off at the top of the hour (if the error was too large the top-of-the-hour reset did not function correctly, and the hour hand was never corrected). This meant that in the event of a loss of power to the clock system, it was necessary to manually reset the hour hand of every clock in the building prior to restart. The convention for Simplex and I believe for other vendors as well is to set all clocks to 12:00 exactly, the master clock then has a mode in which it delivers "accelerated" minute pulses to advance all clocks to the correct time. Back when I was in middle school the controller seemed to be broken in a way where it occasionally went into this mode incorrectly (maybe a short power disruption) and sometimes all the clocks in the building would be moving at 10x speed for a few hours of the day.

DST correction needs to be handled similarly, so you will have to visit every clock in the system at least twice a year, assuming you have reliable power and aren't in Arizona or something. Or, in an underfunded school district, just apply the DST correction weeks late or not at all. It is amazing how habituated people become to the clocks being completely unreliable.

I have read that there were systems that used a third signal to reset the hour hand at 12:00, avoiding this problem, but I've never personally seen one - perhaps they weren't popular at all or perhaps they just fell into an awkward spot at the end of the period where analog systems were being installed. In modern slave clock systems, it's more common to use RS422 or 900MHz radio to directly transmit timestamps once per second. These have the major advantage of making digital displays extremely easy to implement and analog displays still fairly easy, with no need to ever manually set clocks.

In installations today though, it seems like the most popular option for schools are one of several digital (sometimes IP) paging systems that support a clock display as an add-on feature. Integrating the clocks with paging makes more sense than you might think, as the slave clock system in schools generally also controlled the bells (sometimes using the same signal wires, e.g. using opposite polarity of pulses to open a relay on the 12/24vac bells), and so now that bells are being replaced with paging it makes sense to keep clocks on the same system.

There's a subset of the curious internet community of fire alarm collectors who also collect these clock systems, since they are somewhat similar in nature to older fire alarms. I'll admit that I've considered trying to get a few old Simplex slave clocks to fix up and put in my house, probably implementing my own controller since even the later-generation digital controllers Simplex sold were large wall cabinets.