This article is worth reading: http://www.thekrib.com/Chemistry/ammonia-toxicity.html
In short, your tank is not cycled yet. Adding fish to un-cycled tank is at your discretion as you know the potential outcomes.
When I used the 'original' Amazonia + PS it took 2 weeks of daily 90% water changes to bring the ammonia < 0.5 ppm. I believe that most of NH3 and NO3 is actually coming from PS as it's full of organic mater. When I used Amazonia without PS, I never saw the numbers that high. As the organic matter decays, the pH goes down. I think that's the primary basis of the ADA's claim that their substrates are 'designed' to lower pH. In any established planted tank the pH tends to be lower then the pH of the water out of tap even without CO2 for the exact same reason: decay.
PS has virtually no NH4, it's all in the clay aqua soil.
PS has mostly NO3.
ADA As has very little NO3.
PS cannot bind NH4 due to very low CEC, whereas clay has a very high CEC and binds NH4. NO3 cannot be bound easily, hence water changes and issues with ground water.
Peat lowers pH, this is not their design, it's a simple thing folks have used for 60 + years or more in the hobby.
The newer batches of AS have lower NH4.
But can vary batch to batch also.
No matter, large water changes, 2-3x a week are the typical routine for the 1st month or two as you say, then no issues after.