Something really sounds strange here. If it is connected as you describe, there are only two explanations. The installers either connected things wrong, or you have some new advanced system that, I expect, will soon crash on you. Normally the reclaim system will clean the water to the point where you can reuse it for non important functions, such as undercarraige spray. Putting the reclaim water through the softener will shorten its life, probably dramatically. If it doesn't, let us know what you have.