Is this Kinetico plumbed correctly?

I moved into a used home (built circa 2001) back in 2006. It has a Kinetico Water Softener Model 51. The system cycles and I add Salt once a month or so. When I was replacing my hot water heater this spring I noticed my main water input pipe feed both the Kinetico AND my hot water heater. Thus the Kinetico's softened water line is connected to my home's cold water feed and NOT to my hot water heater. In other words, the hot water heater is not receiving soft water.

Is this typical? If not, why would they plumb it this way? Should I consider changing it over my hot water heater to received soft water first? Note my hot water heater died at about age 9. It is a 50 gal gas unit.

Mr T.

It is very stange to soften the cold side only. I have heard of the hot side only, but never just the cold. I would recommend changing it to soften both hot & cold.