A few very expensive pro colorheads incorporate timed shutters above the mixing box to trim off both the warmup phase and afterglow, but we're talking about true commercial enlargers here, big in size and huge in budget.
Yeah, that's the sort of system used where I used to work - the main lab for a large studio chain.
More specifically we used primarily Nord "package printers," equipped with lamp houses from Lucht Engineering. They could expose an 8x10" print in about 400 milliseconds, a bit under a half-second. Here's the operational sequence: the lamp is in a viewing mode - on, but a relatively low power. This is plenty bright enough for an operator to view the negative in the printing gate. When an exposure is initiated the lamp first ramps up to full power. At this point a shutter opens to start the exposure, using unfiltered (white) light. The Lucht lamp houses used hard-cutting dichroic filters, mounted in what were known as "filter paddles" (after the paddle-like shape). Each paddle is mounted on a rotary solenoid in such a manner that the filter can be electrically flipped into the light path. So the light colors are not partially-attenuated, like a typical enlarger would be. It starts out with a white light exposure. Then at the appropriate time each filter paddle flips into the light path, terminating exposure for the appropriate color. Said more plainly, the lamp supplies white light, made up of red, green, and blue light. At the appropriate time, the yellow filter will flip into the light path, terminating the blue-light exposure (a yellow filter passes red and green light, blocking blue). Likewise with the magenta filter, terminating the green-light exposure. When the cyan filter flips in, the exposure is effectively terminated (no light can pass through all three filters). At this point the mechanical shutter closes, and the lamp ramps back down to the low-power viewing mode. Simultaneously the paper advances and the printer is ready for another exposure.
One may wonder, why make a simple thing so difficult? Well, the main advantage is that the machine can individually control the color balance for each exposure. This is actually the same method that was used in optical mini-labs, where they could use color sensors to individually adjust for each negative.
A second, non-obvious benefit was to use what is known as slope control. The users of standard color enlargers generally try to keep a more or less fixed exposure time, so as not to have color shifts related to reciprocity failure. In commercial machines of this sort, including mini-lab printers, a set of printer setup negs (sometimes known as "Shirleys," mainly on the internet) are used. These include a range of exposures, which the operator must individually color-correct. Once this has been done, the machine is able to figure out what corrections must made for various exposure times, aka the "slope correction." So from then on the operator can simply call out color balance settings, and the machine will automatically use the desired filtration, as well as make the corrective adjustments for paper reciprocity failure.
With respect to production capabilities, the Nord machines that we used mostly took nominal 575 foot rolls of 10 inch paper, and could expose the entire roll in around 30 or 40 minutes. So this is about a dozen such rolls in a normal working day - something like 8 or 10 thousand 8x10 inch "units" per day. And we had something like 35 or 40 of these printers in our main lab, which is why I sometimes referred to the lab operation as a sort of "factory" for pictures. As a note, the reason I use the term "units" instead of just "prints" is because they can have different configurations. A package printer is equipped with a set of so-called "lens decks," which can be automatically moved in or out of the light path. One deck might use a single lens to expose an 8x10. Another lens deck might simultaneously expose a pair of 5x7 inch prints on a nominal 7 X 10 inch "unit" (the negative carrier has to rotate 90 degrees for this). Yet another might expose a 5x7 inch print with a handful of wallet-size prints filling out the rest of the unit. All these, or even 10x13 inch prints, all from the same package printer, at the same rate of output.
FWIW these were machines of a past Era. Once digital photography and cell phones came on the scene few people needed wallet-size prints anymore. More adaptable digital printers took over and these older package printers mostly went to the dump, lenses and all; nobody wanted them. Gradually even those printers became unwanted, and on and on.... everybody knows how the story went. As they say, nothing is as constant as change.