The Soviet Union's Nuclear Explosions for the National Economy program was, like the US Project Plowshare, devoted to trying to find "peaceful" for nuclear explosions. These involved things like excavation (diggings holes, canals, and making artificial bays), attempts at what we would today call "fracking," mining underground minerals, and extinguishing underground natural gas fires, among other functions. There were a total of 122 nuclear explosions set off under this program from 1965 through 1988.

One of the first problems they studied was the possibility of using nuclear explosions to create large water reservoirs. This was not for drinking water, but for agriculture: there are areas in the USSR that had good water supplies from rivers in some parts of the year, but would be very arid for others, so creating a place to store water during the wet seasons so it could be used for crops in the drier seasons was a goal. The idea was to basically make craters near streams and use those as sort of artificial lakes. The first test of this program, Chagan, created such a lake in Kazakhstan.

The weapon used to do this work had a very low fission content; some 5 kilotons of fission energy was used, with the rest (135 kt) of the energy coming from fusion. The goal here was to minimize the amount of fission products, which are the long-term contaminants from nuclear detonations. Even so, the Chagan crater still got fairly "hot" and is still radioactive to a degree to this day, and the water, at least in 1998, was still at levels of 300 pCi/liter, which is some 20X higher than EPA drinking water standards for alpha emitters.

In later tests, they did three experiments in 1969-1970 with creating entirely underground craters, as studies for potential water storage. The results appear to have been unsuccessful in one way or another as they did not use them for water storage nor did they do any further experimentation along these lines. Again, these were not drinking water reservoirs, but agricultural use. There are reports that the "water reservoirs" bit was just a cover story in any event, and that they were instead studying the use of the facility for underground megaton-range explosions.

You can read much more about the Soviet PNE (Peaceful Nuclear Explosion) experiments and history in this article, which is where the details above come from:

• Milo D. Nordyke, "The Soviet Program for Peaceful Uses of Nuclear Explosions," Science and Global Security 7 (1998), 1-117.

In sum, I think the commenter is incorrect (either through memory or just being told something wrong) that the Soviets ever used this to actually create reservoirs for drinking water. They did explore the possibility of creating water storage in arid regions for agricultural purposes, but never deployed it on a large scale. It is not impossible that you could have the radioactivity be low-enough for many purposes — it is a matter of your fission to fusion ratio in the weapon, and presumably on how much water is used (as it dilutes toxins, etc.). But as the US found in its own similar program, the problem of contamination does add to the cost and difficulty of the whole approach, and generally it doesn't work out in favor of it.