When my 16" chain got pinched on a big branch and subsequently flew off the bar it damaged several drive links.
I decided it was best to just buy a new chain instead of risking damage to my chainsaw; the chain is considerably less expensive than my chainsaw. It's also considerably less expensive than a damaged body part.
Remove the chain completely from your saw and inspect every inch of it. If something looks bent then it's not fitting into the sprocket properly and you'll be buying a new chainsaw in short order.
I cannot comment on your claim about proper tension since you provided no pictures.
Your chainsaw manual should have tensioning instructions. There are countless YouTube videos on the subject as well. If you bought a cheap homeowner-grade chainsaw then it's quite possibly just a crappy chainsaw and the chain will always fly off.
In general you should be able to tug on the chain and it should snap back and hug the bar. It should be difficult (not impossible) to derail the drive links out of the bar.
https://www.oregonproducts.com/en_ca/chain-tension