No need for the putty there, the rubber washer will seal fine against the sink.
The problem is the rubber washer isn't sealing the threads so that is where the leak is coming from. Water is seeping down through the threads.
Do not use Teflon Tape! But do apply Teflon Paste such as Rectorseal T+2, Megaloc, or other brand, to the threads that will be running inside the Mack washer when tightened...
This will cure your leak... Guaranteed!