sorry to hear what happened. Be certain to protect yourself, especially your eyes.
The pH of a typical dosing solution is above 14. At that pH, the hydroxide reacts with fats in your skin, converting them to fatty acids. That disrupts membranes and damages cells. Other things happen too, but that’s the one that causes the slippery feel. That reaction is the old way of making soap: fat + lye —> soap + glycerol.
Once in the tank water, the pH is below 9, both from dilution and by reaction with bicarbonate to reduce the hydroxide even more, forming carbonate. That pH change has lowered the hydroxide concentration by a factor of several hundred thousand. The same reaction likely still proceeds to make fatty acids, but several hundred times slower so that it is not noticed.
All of the other effects of hydroxide are also greatly reduced as well, and you don’t get the same sort of cell damage putting your hand in seawater.