Stopper won't hold water in new bath sink

A plumber installed a new 19" round bathroom sink in the vanity. Same size as the old sink. We kept the same faucet and drain. The stopper is the lift rod to close drain, push rod down to open drain. The plunger won't hold the water in the basin. Called Moen, they sent a new plunger, and it won't hold the water either. The plumber doesn't know why. Has anyone got a remedy for this, a new sink that won't hold water is useless. Do they still make those old push in rubber stoppers?

My guess is that it's leaking between the drain and the porcelain into the overflow cavity.

do you mean the water's going out from under the metal drain collar?

Yes. My guess is the plumber didn't seal it well enough. Easy enough to test with a $1 rubber stopper.

Do you know how I can fix it? I'm a 66 yo female non-plumber.

Assuming the stopper and the rod has been removed, do as follows:

Loosen the jam nut under the sink so that the trim can be unscrewed from above. Roll some Plumber's Putty in your hands to warm and soften a finger sized length and form it into a donut under the trim. Screw the trim back into the drain. Tighten the jam nut underneath. Clean up the excess putty that will mush out from under the trim.

You're right, I bought the plug and the water still seeps outs. I'm going to call the plumber to come back, he should have known that, he's been doing this for many years. My thanks to you for helping.