There are two very different issues here, and they need to be dealt with individually. One is the pH, and the other is the nitrogen cycle (ammonia, nitrite, nitrate).
Taking the latter first, do you know about cycling a new aquarium? There is a section here for cycling, and this article in particular will help you understand it:
http/www.fishforums.net/index.php?/topic/421488-cycling-your-new-fresh-water-tank-read-this-first/
A new tank has to be cycled. I prefer doing this with live plants, but there is also the fishless cycle as explained in the link. During this period, the ammonia, nitrite and nitrate may well fluctuate, as the article will explain.
Now to the other issue, the pH. This is related to the hardness of the water, what we call the GH (general hardness, which is the measurement of dissolved minerals in the water) and the KH (carbonate hardness or Alkalinity). The pH will usually be relative to the GH and KH. I won't bog this down further, but move on to your testing.
Tap water usually contains dissolved carbon dioxide. The CO2 acidifies the water, which lowers the pH. But CO2 can dissipate out of the water fairly easily, as this results in less carbonic acid and the pH rises. In orer to obtain a more accurate pH test of tap water, you should out-gas the CO2 first. This can be done by letting a glass of water sit 24 hours, or more quickly by briskly agitating the water for a few minutes. Then test the pH.
When the water is added to an aquarium, the pH will likely settle out within a day to the same as the tap water (with CO2 outgassed). The initial GH and KH of the tap water also play into this, as the KH in particular tends to "buffer" the pH, preventing fluctuations.
If there are calcareous substances in the aquarium, meaning sand/gravel/rock composed of minerals such as calcium, magnesium, limestone, marble, coral, shells, aragonite, dolomite and a few others, these will slowly dissolve, raising the GH and pH. And in reverse, organic substances (wood, leaves, peat, and in time fish waste, etc) can work to acidify the water and lower the pH. The initial GH and KH are factors in this as well, affecting the degree to which changes may occur.
So, in addition to properly testing the tap water for pH, you should also ascertain the GH and KH. This you can usually do from the municipal water authority, on their website or by calling them. Once you have these numbers, we can discuss all this further.
Byron.