I used a pH meter for Aquariums in my experiment. May be the pH paper for urine testing is not accurate enough for water testing.
But anyway it looks like distilled water can rapidly become acidic because it reacts with atmospheric carbon dioxide and even in 24hrs you can expect a pH of 5.5-6.0
Fresh made distilled water should have a pH close to 7:
“We are often asked about distilled water and pH. The rule of thumb is that distillation will always move the pH closer to 7, which is neutral. This is because distillation removes all contaminants, whether acid or alkaline.”