Wasn't quite sure under which topic to post this, but this seemed closest.
Is it true that water should not be used in a house at the time the water softener is running, and if so, why is this?
Yes that is right. When a single tank water softener is going through a regeneration cycle it by-passes itself and hard water is supplied to the home. Also during the brining cycle if water is used in home you could get salty water in plumbing lines. That is why single tank softeners are usually set to regenerate 2am.
This is the logic behind two-tank systems. When one tank is exhausted, the unit switches to the other one while the first one recharges off-line. No unsoftened water at any time with those designs.
Single resin tank softeners... hard water while regenerating
Twin resin tank softeners... soft water 24/7 (all the time... even while regenerating)
The question you should have asked is... with the (insert brand and model of your softener here) I have or am considering buying is it true that water should not be used in a house at the time the water softener is REGENERATING?