If you really think this is the case, try the following, which will be a little more controlled:
Mix up a fresh batch of salt water, let it sit for a day. Prepare a few samples of newly prepared water mixed with tank water and test at different mixing ratios. E.g. 100% new water, 0% tank water; 75% new water, 25% tank water; 50% new water, 50% tank water; 25% new water, 75% tank water; 0% new water, 100% tank water.
Doing this in isolation will tidy up a few variables, like water mixing, alkalinity consumption, etc.
Is there any chance that you're missing the end point on the titration, or not cleaning all of your testing supplies between tests (with rodi)? Those can both throw things off.