[Dr Colliebreath]

You should be ok with the 20 gallon filter on a 10 gallon QT. Which model filter is it?

You should be able to quarantine those fish in the 10. Just put the filter media (floss pad and biomedia, if you have both) in your DT for 2 weeks (another week or two won't hurt) and then put them in your QT filter and put fish in the QT at the same time. Monitor ammonia and manage it with water changes if necessary.

Put a couple of small pieces of pvc in the tank for hiding places.

You have a top for the QT, right? You don't want to lose fish to jumping.

By the way, multiple chromis frequently fight until only one is left.