The recommended dose of Prime and/or Safe are based on fixed amounts of disinfectant (chlorine/chloramine), and due to them both being reducing agents, yes they will reduce 02 levels once there is no longer any disinfectant to reduce. The dosage rates that I posted are from years back, which IMO are more accurate than what they currently have listed on their labels. At those dosage rates, all chlorine is reduced, and all free ammonia is neutralized.
Having said that, without knowing ones residual at their taps, it's pretty much a case of by guess or by golly.