LOL, good question - most people wouldn't bother...
There's quite a big difference between spring water, tap water and distilled water.
In theory one should replace evaporated water with distilled water if one would have a closed system that doesn't have anything in it that consumes minerals(ie grows). The whole thing becomes quite complicated when one has plants, bacteria, algae,animals and adds food to the animals.
The question would then be is the evaporation rate together with the added amount of the mineral(food) enough to to concentrate a specific mineral despite its consumption rate.
I would say that what "kind" of water you should add depends on how much and which animal/plant/bacteria etc poplations you have in the tank, the volume and type(previously) of water, the volume and type of substrate, gas-exchanges etc etc.
I started out thinking like that but after a while I gave up since nobody really knows and it would take a lifetime to find out.
Me, I use tap water
.
I you are worried, never just replace the evaporation but do a very small water exchange at the same time.
A tip, if you are high on minerals in general algae will love the tank. If you are low on minerals in general growth in the tank will be slow(PO4(3-),NH4(+)).
It is a good thing to have fast growing plants, they show you very clearly how the status of your tank is through their growth.
What I am trying to say is that if your tank has clear water with very little growth you really shouldn't add distilled water on the other hand if you have a tank that is all green - go ahead and add distilled water.
Sorry if repeating things you already know...
LOL, this text is probably loaded of errors...