In my previous post I explained how things work with respect to pH and hardness. Whether or not you need to adjust depends obviously on the needs of the fish you want and the existing tap water parameters. When you've posted those it will be easier to say if adjustment is necessary, and if so, how to best achieve it.
With respect to the blind cave tetra, the information in our profile is accurate. I can say this because I wrote it; and in writing these profiles I research the fish species thoroughly and use the consensus; where there is significant difference from reliable ichthyologists I mentioned it. Given the origins of this fish, one would expect the water parameters preference to be basic and hard (as for livebearers), and that is borne out by the info in the profile.
Some fish are adaptable but this varies with the species and their origin (wild caught versus commercially raised). Again more can be said about this if necessary when the parameters of your tap water are know.
last comment on Ponyo's point about stability and water changes. Here again, this partially depends upon the parameters of the source water (tap water for most of us) and where you want the aquarium water parameters to be. Once an aquarium is biologically established and stable (this takes a few months, not to be confused with cycling which is a very different thing), the "stability" in the tank will tend to keep things stable water-wise. Partial water changes using tap water with different parameters will not normally be an issue, unless the difference is major and one changes more than 50% of the tank volume. The "stability" that settles in every aquarium works if it is not fiddled with; this is why I regularly advise planted tank beginners to go low-tech--minimal interference by the aquarist with more reliance on nature to do its job will lead to more stability.
Hope this helps explain things.