Distilled water is bad for aquariums on its own. It doesnt contain any of the minerals etc necessary for a healthy aquarium. It has zero (or at least very low) general hardness (GH) which would suit fish that prefer softer acidic water, but wont suit fish that like harder, higher pH water. It also has zero (or at least very low) carbonate hardness (KH) which can effect your aquariums ability to cycle, might effect plant growth, and will provide no buffering against pH fluctuations which are bad for fish.
If you use distilled or RO filtered water you need to add those minerals and carbonates/ bicarbonates back into the water. Normally this is done by adding buffering salts, or you can mix distilled with tap water so it gets those minerals from the tap water proportion. This is commonly done when you need to tailor very specific water parameters for your fish, or if your tap water is very hard and you need to soften it.
I cant comment on what was discussed on another forum as to what lead them to suggest distilled water. Nothing you have raised so far on this thread leads me to suggest distilled water is necessary, but maybe you provided information to this other forum you havent done here.
While this may not be related to your fish deaths it is something that should be considered. The lack of minerals may have caused an unhealthy environment for your fish. The lack of KH may have lead to fluctuating pH levels that stressed the fish. Maybe the addition of algaefix compounded issues.
Ive done a little reasearch on how algaefix works. It does indeed use a lot of oxygen in the process of killing algae. Lots of algae die off, more oxygen depletion. Did the algaefix have any positive effect on your algae?