Perhaps there is an easier way to show this. With the same hypothetical example, imagine:
1) 11 gal worth of TDS in our 10 gal tank
2) After 1 gal evaporates, we now have the same 11 gal of TDS in only 9 gal of tank water
3) We remove 50% of the tank water, now leaving 5 1/2 gal of TDS in only 4 1/2 gal of tank water
4) Finally ,we add back 5 1/2 gal of treated tap water, restoring our TDS to 11 gal worth and our tank to 10 gal, bringing us back to our original concentration.