Water only comes to chemical equillibrium with its container. The water obtained from well has often been in the ground hundreds or sometimes thousands of years. It acquires dissolved minerals in this time, which make it taste a certain way.
When water is stored in plastic containers, the only thing that can really happen to it is transfer of chemicals into or out of the water. HDPE (high density polyethylene) is one of the best (most inert) for this porpose.
Still, if you have water stored in a garage for a number of years, that water will eventually acquire the taste of petroleum, etc. that was also in the garage. Vapors can seep through the plastic given enough time.
Basically, don't worry about it. The exact taste of water in long term storage is fairly unpredictable (some of the minerals that make it taste good might settle or plate out, leaving stale tasting water). Just keep some bleach or other disinfectant on hand to make sure any opened water stays safe to drink.
Scott