Kimchi in Mason Jars -- Too Sealed?

If your jars aren't in the refrigerator already, I highly recommend unscrewing the lids as soon as possible...unless you want to be able to share stories about how you found glass shards and the smell of kimchi everywhere in your kitchen one day.

Depending on when you mean to eat them, I'd recommend a mix of room temperature ripening and fridge storage. Keep the lid completely unscrewed while at room temp until ripened to a stage you prefer, and keep it loosely on in the fridge and eat it up in the next few weeks (where it will continue to ferment some more but slow down drastically). It's not a terrible idea to put something like a sheet pan under the jars just in case one overflows.

Cheesecloth is overkill, but you could choose to use that or anything that'll cover the top of a jar without making it airtight while at room temp. Glass jars are used often in commercial kimchi production and sale, so other than making sure the lid isn't fully screwed on they're fine to use. The explosion concern is mostly when you leave it too long (more than several hours?) at room temp or in the fridge for more than a couple weeks - while the jar is completely sealed.

This all depends on the kind of kimchi you are storing, of course. I'm assuming it's the freshly made napa cabbage type you're talking about. Some kimchis don't ferment as much or at all.

I am a bit late to be of use to OP but had to add that in my almost-50 years of native Korean kimchi experience i've never heard of a kimchi jar explosion at room temp - at least not the kind where you see pieces of glass and kimchi all over. The most that happens is juice overflowing the top of a plastic lidded jar. A mason jar with a tight metal lid I'd expect loosening of the lid and overflow and/or the gas warping the metal lid upwards into a slight dome. Unless one needs a lot of mature kimchi quickly, standard practice is to leave at room temp for a day or so, then move into fridge. Also, less contact with air is better for pleasant fermented taste. In the olden times palace chefs would make numerous smaller jars, to open a new one for each of the king's meal.

When making kimchi (or other fermented products like it) it's best to ferment the whole batch together for the first phase (this depends on what you're making, how much of it you're making, and how sour you want it to be - but a week is a good rule of thumb). This helps to make the whole batch more consistent, as one batch will ferment at the same pace - as opposed to many small batches fermenting in different ways - and in general will cut down on variables which is always a good idea when fermenting.

When I make kimchi, I usually make 5-10 liters at a time and put it all into an appropriately sized jar. If there is extra headspace, you have a few options, the easiest of which is to take a clean plastic trash bag, put it into the jar and fill it with water, then tie/close the bag so the water can't come out. This will make it so no oxygen comes into contact with the top layer of kimchi which should ideally be submerged in its own juice at all times.

I leave the jar in a slightly cooler than room temperature room, in the dark (or at least wearing an old sweatshirt so no light gets in) for 1 week to 10 days, then fill smaller bottles and store them in the refrigerator. At this point they can be given away to other kimchi lovers, or kept in the fridge for ~6 months (probably longer, in fact, if they're not opened, but I've never gone longer than that - and in fact it's rarely lasted that long).

In your present situation, I think you'll be fine opening the lids just a bit, but if you're storing them in the fridge there should be no worries at all - it won't continue fermenting in so cold an environment.

I normally pack it in, leaving maybe half inch of headroom, barely tighten the lid on so gas can get out (have your fermenting jars on a tray to catch leaking during this time). Then after two or three days i unscrew the lid, wipe the threads and lip off the jar with a clean damp cloth, clean my lid, then tighten them down firmly. I think if you use the plastic lids you can skip all of this and get a nice carbonated product at the end, but I normally have the metal lid with the separate collar. I've been making kimchi for a few years, and I always leave it in my cupboard for weeks or months till I'm ready to open it. These people talking about explosions or putting it in the fridge after a couple days don't know what they're talking about.

I have been making kimchi and putting it in mason jars for years. I have never had one explosion no matter how fermented it has become.

My hypothesis is that you don't really need something to push the kimchi down to prevent it from oxygen if you just carefully bleed a little bit of pressure from the jars in the beginning of fermentation. The active bacteria and yeasts will secrete CO2 which is heavier than air and you will bleed out the air on top, leaving a covering blanket of CO2 on top of the kimchi, protecting it from oxygen. At least this is common practice when fermenting and kegging beer.