I believe you are to install the plug the first time using the wrench. You install the plug and firm it up as snug as you can with the wrench and your hands. Then loosen the plug with the wrench and afterward use the plug just as you normally would - no wrench.

I think the wrench is to apply enough force to fit the seal at the end of the plug to the barrel. Once that seal is established, it's finger operation from then on.