You will use RO or distilled water in the drop checker.
The pH of the tank or tap water is not important as far as the functioning of the drop checker.
How a drop checker works:
CO2 dissolves in the tank.
The drop checker is set up under water, to take in air only from the tank water, what evaporates or out gases from the tank. It is not in contact with the room air (Except the little bit from its initial set up). So whatever CO2 is in the tank gets into the drop checker. When there is more CO2 in the tank water more CO2 finds its way into the drop checker. When the CO2 level in the tank drops some of the CO2 in the drop checker re-enters the water.
The solution in the drop checker is very carefully set up so the ONLY material that dictates the pH is the carbonates and the CO2 from the tank.
When those 2 materials are the only things that alter the pH in the drop checker, then you can use that pH change to tell reasonably closely what the CO2 level is in the tank.