If your tap water has no phosphate, nitrate, copper, zinc, cromium, silicates, or tin then it's probably safe to use but I would still agree that if you can get distilled to use it. You might also consider buying an RO filter yourself. If the water really is that good then the RO membrane will last a really long time.
I tend to do water changes during the cycle to keep ammonia below 0.5ppm. This keep more of the life that's inside your live rock alive and has long term benefits. Super high ammonia levels during the cycle can create a nusiance algae issue that can be frustrating to resolve.
I would not even test PH during the cycle... it will fluctuate wildly during the cycle and if you try to fix it there's a good chance you'll just be wasting your time (best case) or cause damage (worst case).