You must have been trained after speed loaders became common.
Were you ever issued a dump pouch and/or bullet loops?
View attachment 781955
View attachment 781956
I was issued a leather double dump pouch like you show. I had to go out and buy a speedloader carrier (and speedloaders) on my own dime. (I occasionally used the double dump pouch for speedstrips.)
At that time a lot of the older guys & gals wore Buscadero gun belts, and the belt loop styles varied. Some had a full line of them across the back of their belt, and some half a line on their strong side behind the holster. Most of them also had speedloader carriers sewn to the front (primary reloads). Some had a double loop just above and in front of their holster, so they could 'top off' if they'd only fired a couple shots. Reminded me of an Old West practice.
In those days the qual course-of-fire included a section where everyone ran (joggled, whatever) from 50yds to the 25yd line, and then fired 10rds. The time limit was 25sec, and the clock started at the 50yd line "GO" signal. The last 4rds could be loaded from loose rounds, belt loops or a partially loaded speedloader (my choice

). Since both Colts and S&W's were being used, the shooter had to know the direction the cylinder turned so the last 4rds would immediately come up under the hammer. 25sec may sound like a short time for all that movement, shooting and partially reloading a revolver, but it was a rare thing for someone
not to get off all of the rounds before the whistle blew.
Years later, long after we'd transitioned to issued pistols, I still included different loading methods for my snub quals and drills, using speedloaders, speedstrips and loose rounds. The trick is to keep those old revolver skills from completely fading away from disuse and rust, and not having to 'stop and look & study' what you're doing with the gun to the point you're no longer remaining aware of what's happening around you. Not much different from the days when they drilled everyone to perform 'tactical reloads' of pistols to keep them hot and fully loaded between positions, moving and taking cover, etc. Sure, in later years it seemingly became a 'thing' for different folks to talk about 'speed tac loads' (dropping partially loaded magazines in order to replace them with fresh mags), and 'reload with retention' (keeping the partially loaded mag for later). You could always tell the more experienced (older) folks when they were performing tac loads and keeping the partially loaded mags without stopping to think about it while they were busy with other needs of the moment.
Of course, the circumstances will likely dictate the best 'options' desired. If you have more than a single speedloader, speedstrip or sectioned belt carrier (2+2+1/2+2+2), and you've fired more than 2rds, you might end up choosing to just quickly reload the whole cylinder instead of topping off 1 or 2 spent rounds. TANSTAAFL.
The trick is to have the requisite skills for any/all of those options ingrained deeply into the 'unconscious competence' level.

That typically takes time and successful repetition.