That acclimation is not my favorite method. If the fish have been in the bag less than an hour, should be fine though.
Okay, for qting some fish and not others, that is not always true, but can be. For instance, if your clowns were captive bred and never introduced to any system with wild caught, they they would reasonably speaking not need to be qted. That goes for any captive bred fish. Now, fish stores have a habit of putting fish in same tanks with wild, so qt would be necessary for all fish.
Look at the pictorial above to identify what you may see on the fish. That is a good guide. Pictures for us should be in white lights as the blues we cannot see well.
Next, yes, adding 8 fish into the 60g could have been part of the problem, but not because of the system bacteria per say, more because of the disease and stress on the fish. Then if one dies, the lack of sufficient bacteria can come into play.
I know you want the yellow tang to survive, so the best idea is get all fish out and qt them. Use some meds as needed (careful which ones due to wrasse). Leave the main display with no fish (fallow) for up to 76 days. This will rid the tank of parasites.
Good luck!