We use tap water but it goes through a reverse osmosis filter at the tap in the sink (at the "point of use"). We wash out suggie water cups every morning, rinse thoroughly and put new "filtered tap" water in every morning.
Reverse osmosis does takes out chlorine and other chemicals "at the point of use," - but it is not meant to be stored for long periods of time but rather generally consumed within hours. If we were going to store water for a camping trip or a survival bunker, well then we'd use the tap in the laundry room that's deeper for big jugs and with plenty of chlorine.
Reverse osmosis also takes a whack at microbes that pass through the reverse osmosis membrane, too. So by reducing both the microbes and the chemicals at the same time, you end up with something a little closer to... water.
If you use this reverse osmosis "filtered tap water" for your pets, so long as you refreshen it each morning the liklihood of microbe build-up that is hurtful (overnight) is a small risk. They are more likely to contract something from your hands for lack of washing or from containimated food than from freshly filtered water.
But if you do not have this type of system, chlorinated tap water is probably a better choice than generic bottled water.
Unless you pull water from a private well, you can contact your local water authority and it is typical that they publish an annual "water quality report" that lists all the wee beasties, toxic chemicals and metals that are in your water. The EPAs guidelines on what is "acceptable" is usually a main topic of discussion in these documents. But not on the labels of Fiji.