I rub putty on the threads where it fits though the sink. Water will follow the threads otherwise.
I have installed a new (plastic) pop-up drain with overflow into a integral lavatory and counter fixture.
The plastic gave me some fits getting the drain fittings aligned to not leak, but I finally got a no leak flood test up to and into the overflow.
An hour later there was a small puddle under the drain.
Given the testing I did as I resolved the original leaking of the drain assembly I'm betting there is water hanging up between the drain escutcheon and the underside rubber gasket that is not making its way into the overflow hole into the drain. It is pooling in the overflow cavity and finding some small gap to leak out.
I did clean the lavatory drain holes top and bottom prior to installing the new drain.
Any suggestions on what can be done to get a water tight seal at the rubber gasket below the drain's overflow hole?
Throw that plastic drain assembly away & go get a brass one, then follow Terry's advice.
I pressed putty in the threads of the drain pipe that passed through the rubber compression ring and smeared putty onto the top of the compression ring.
No more drips.