3 fish, 2 of them tangs in an un-cycled, unmedicated tank is a big risk.
The tangs are going to be so stressed their immune systems weaken. Anything goes wrong like short spike in ammonia or other minor water quality issue it will wipe them out. Could be why the blend made it.
In the future you may want to look at your quarantine process and equipment to minimize the risks. Relying on water changes is extremely difficult to balance even for the most experienced aquarist. IMO it’s better/easier to have a well cycled system as a starting point.
The tank has 2 grapefruit-sized pieces of live rock from my LFS, so the tank should've been able to handle the ammonia even if I didn't cycle the tank ahead of time. In fact, the API ammonia test was near-zero for 5 days straight when the tangs died, so I didn't do any water changes. Maybe it
was velvet.
In the future, I'll treat everything with copper using Jay's method. I'll replace the 2 live rocks with multiple bags of Matrix which I'm currently seeding in my DT. Hopefully they'll be sufficient to keep the ammonia down since I can't use live rock or calcareous sand.