For those who are interested in the chemistry, keep reading. Otherwise, skip it.
I am not a chemist, but I did take three years of chemistry during my Chemical Engineering curriculum, so I understand basic chemical reactions.
Sodium thiosulfate is the basis of most aquarium water conditioners. It is a potent reducing agent. Back in the days of optical camera with film, photographers used sodium thiosulfate, which they called photographers hypo, to dissolve silver bromide on the film and photographic paper, fixing the exposed image.
In aquarium use, sodium thiosulfate reacts with chloramine to split the compound into original chlorine and ammonia parts. Since thiosulfate is a reducing agent, it will reacts with chlorine, which is a potent oxidizing agent. The result will be::
Na2S2O3 + 4 Cl2 + 5 H2O = 2 NaHSO4 + 8 HCl
Thus, the result of the oxidation-reduction reduction in the presence of water will produce sodium bisulfate and hydrogen chloride, both of which are acidic compounds, but in weak concentrations are not harmful.
Sodium thiosulfate does not react with ammonia directly. Ammonia gas (anhydrous) has the formula NH3 and is extremely toxic. When dissolved in water, the ammonia combines with the water molecules to form ammonium hydroxide NH4+ OH-. However, since the pH of an ammonium hydroxide solution is quite high, most of the ammonia present will exist as NH3, except in extremely dilute concentrations such as, hopefully, will be the case in our aquariums.
While ammonium ion NH4+ is less toxic that ammonia NH3, it still cannot be considered non-toxic.
If you go back to the original reaction of sodium thiosulfate with chlorine, you see that is will produce two compounds that are acidic. Those compounds will react with some of the hydroxide ions of ammonium hydroxide, which is a good thing, but since the hydroxide ions associated with the ammonium ions are only a small percentage of the overall hydroxide ions in solution, it will not have a major impact upon the balance of ammonia and ammonium ions unless the pH close to neutral or even acidic as it would be in a black water aquarium.
In a fully cycled aquarium, the addition of a small amount of ammonia should not pose a significant issue as the nitrifying bacteria will soon begin converting ammonia to nitrite and the to nitrate. However, for aquarium that are at high pH levels (above 7.5) you might still have a short term spike in ammonia levels if you do large water changes such as 50% at a time. If the tap water contains 1 ppm ammonia as chloramine, you would spike the ammonia level to 0.5 ppm with a 50% water change. While this might not kill the fish, it might irritate their gills.
Water conditioners such as Seachem Prime and
Kordon Amquel Plus claim to detoxify ammonia and other nitrogenous compounds. However, the formulations for such products are considered proprietary, so the exact mechanism of this detoxification has not been revealed. I presume that these water conditioners contain organic compounds that react with ammonium ions to form quaternary ammonium salts (aka amines). As the reaction removes ammonium ions from solution to form the amines, some of the ammonia (NH3) in solution would become ammonium ions to restore the balance between ammonia and ammonium ions in solution at the given pH. Thus, it is entirely plausable that the water conditioners are functioning as advertised.