Is this soil from pots indoors/outdoors, is it already in a bed?
Absolutely nothing wrong with storing the soil in totes, it'll work out just fine, make it easier on you to keep things moist until re-use in fact due to the humidity being trapped inside of the totes.
That said? You can legit just leave the soil wherever it is and you should be fine. Consider it a test of the IPM in your soil, as well as the quality and size of the soil web itself.
Unless I need to dump the soil for whatever reason, I just leave it wherever it is. If it is in pots, and I won't need the pots for weeks/months, I just keep watering the soil. Of course, you'll need less water than normal since there's no plants to drink the water.
But my point is, if your IPM and soil-web is truly on point, you should be just fine leaving it where it is and simply keeping things moist enough.
This is an easy fact to forget, but many microbes simply go dormant as opposed to actually dying. We can use that to our advantage.
Only provide enough water to take care of the soil web, and nothing more. Bugs need water, much more than microbes do in fact. Someone else mentioned covering the soil with sand, perfect suggestion.
Controversial as this sounds, fact is, if you can't rely on your IPM for things like this then your IPM needs some work.
IPM is so much more than just the amendments we use (Neem, Crab/Crustacean Meals or Insect Frass for chitin, etc.)
IPM also consists of companion plants, and good bugs as well.
True and reliable IPM is all but impossible if you are not making your own EWC, unfortunately.
Terpenes are the most popular form of communication, yes? Imagine your soil literally "vibrating" frequencies, but in the form of smell/terpenes. A healthy enough soil will legit "send signals" for all the "good guys" to respond to while simultaneously sending signals to deter the "bad guys". This is exactly why, after multiple cycles/seasons of organic growing, our soil always happens to be filled to the brim with "good" bugs.
Good rule of thumb? The microbiology in your soil is directly proportional to your bug population in the soil. If you're seeing good bugs every time you move mulch around, the microbiology is even more impressive. No bugs when you move mulch around? Your soil likely still needs some work.
A proper soil web has a perfect immune system. However, much like with us humans, its difficult for this immune system to work properly if we're putting crap into the equation. Whether its synthetic nutes (not dogging on hydro, synthetics kill microbes. That's it), or McDonalds/TV dinners.
Neem + Chitin, silverwings, pill bugs, centipedes, predator mites, predator wasps, and companion herbs (chives, basil, dill, rosemary, etc.) will ensure minimal pest problems, if any at all. The caveat to this is that it takes time to establish a soil web/environment with the aforementioned IPM. Once established? Soil becomes damn near impregnable. And if we achieve a soil web of this quality and magnitude, but still have pest issues then the issue is likely elsewhere and has nothing to do with the soil itself. Something else got thrown out of balance along the way.
The goal of living soil is to minimize human input to nothing more than watering (or irrigating, ideally). All of the players in the soil equation (bugs, microbes, etc.) have been perfectly designed to work in harmony with plants, which have also been perfectly designed to thrive and survive.
The more we submit to the naturally designed simplicity, the greater our results.
Like I've always said, I'm a shitty grower, I just fully and wholy submit to the power that living soil+plants were designed with and don't try to fuck with them. These microbes have largely gone unknown/unnoticed for centuries. We have barely scratched the surface of microbiology.
"According to a new estimate, there are about one trillion species of microbes on Earth, and 99.999 percent of them have yet to be discovered.
As recently as 1998, the number of microbial species was thought to be a few million at most — little more than the number of insect species. But estimates have been growing ever since."
Source:
https://www.nytimes.com/2016/05/24/science/one-trillion-microbes-on-earth.html
All the best!
tl;dr: If practical, leave the soil where it is, keep it borderline moist so bugs can't survive but microbes can. Totes will work perfectly otherwise, however the soil web will be destroyed twice doing so. Web gets broken apart once dumped into the totes, and then broken once more when the soil in the totes are re-used in pots/beds/etc.