The active ingredient in Tetra Algae Control and API Algaefix is a surfactant (think: soap, although not exactly). Surfactants alter surface tension which, in the case of fish, disrupts the ability of their gills to absorb oxygen. It is known to cause problems with fish.
It does work on algae, by causing the cells to burst, and fish do adapt to it. At full dose, though, the sudden change can kill some fish. The algaecide effect can still be accomplished by dosing half the recommended amount and then dosing the other half several hours later. This reduces the stress on fish. It also helps to heavily oxygenate by ensuring strong surface rippling when using these products.