Unlikely Hydrogen sulfide and nearly 100% not fault of the anemones. BTA's can go thru hell, they can die, and still it is unlikely that they would kill fish that fast.
The only thing I can think of that is naturally capable of killing fish that fast is toxin from medusa worms.
Look into it, it essentially prevents them from being able to breathe.
Did you start with Live Rock or dry?
Toxin from medusa worms can be directly linked to fish deaths yet inverts surviving, as their toxin has no effect on shrimp/crabs corals etc.
Even the fastest acting marine diseases that I am aware of don't turn fish from healthy to dead in a couple hours.
They aren't commonly discussed anymore, but I found a few in one of my tanks last year.
Warning: Why you shouldnt buy a Medusa Worm New to the Hobby
www.reefcentral.com
Heres a old article about them.
They can be very small.
There are certain species of marine cucumber that can also release a similar toxin, though they are usually a little easier to spot in the tank.