Your worry that "purified" water might drain minerals from your body is an issue that concerns purified water obtained via distillation. In the case of eSpring, the water is treated via filtration using carbon filter together with UV sterilization. Technically speaking, purified water refers to water obtained via distillation or reverse osmosis. Filtered water is not purified water, so to speak.
The eSpring water purifier features a UV light and a carbon-block filter, which it claims capable of reducing more than 140 contaminants whilst allowing the beneficial minerals like calcium and magnesium to pass and remain in your water. The UV light works by reducing microorganisms in your drinking water, all done without any chemicals.
You should not worry too much about minerals being drained from your body even if it's water obtained via distillation. Whilst pure water helps to remove minerals from the body that cells have eliminated or not used, it does not "leach" out minerals that have become part of your body's cell structure.
In any case, your body obtains only 5% of its minerals from water. 95% comes from your food intake.