A salt exchange softener is not a good thing to use for fish. <Esp. Sodium salt exchanger.>
What the ion-exchange softener does is to exchange Na for Mg & Ca. And it has to add 2 of Na for each Ca/Mg to maintain electrical neutrality. Us humans call water rich in Ca/Mg hard water, so removing them is good enough for washing & such. However, fish sees the osmolarity (ie the amount of "stuff" in the water). Ion-exchanged softened water actually has higher osmolarity than un-softened water (because it is full of sodium), so it is worse than using your well water plain.
If you well water is really bad, you can mix in reverse-osmosis water. This softening process removes all the ions, without adding any salt back in, so is a much better source if you want to doctor your water. However, unless your well water is REALLY bad, it is generally better to stick with unadulterated tap water. <less chance of errors, no risk of pH crash, etc.>