I’m not sure of exactly how the physics of an RO units works, other than water if forced thru a semi-permeable membrane. :notsure: But I think I can help you with your other question..
As far as hook up, I have seen many different versions of these units. One version is connected directly to your plumbing, most people set them up in their basement or garage. There are also other smaller versions that can be attached to a facet, but these generally have a smaller out-put
As far as water on demand, you do have to wait for the water. The production, or flow is usually measured in GPD, gallons per day. This site sells units rated at 35,50,100 and 200 gallons per day. So for example, if you bought the 50 GPD model, and you needed to fill a 100gal tank, the unit would have to run for 2 days to produce the water needed.
As far as a tank, Most people have a separate tank or barrel that the RO units fills so that they can produce water ahead of time, so it is ready when they need it. You usually don’t want the RO unit to dump right into the tank anyway because the water produced has to be treated first (i.e. salt added, heated to correct temp, and any necessary pH buffer added)
Hope this helps…