It the putty fails water leaks from the tub into the drain but not onto the ceiling.
Jacuzzi tub drain stopper leaking.
Carefully remove the cover plate and extract the connecting rod and spring up through the overflow opening.
Put the stopper in the tub and fill it with a small amount of water.
Pull up the tub stopper and remove it along with the attached rocker arm from the drain.
With these you will need to extract the drain stopper and rocker arm from the drain opening in order to free the spring.
The only thing that needs to seal on a tub drain is a clean rubber seal between the tub and the drain shoe.
If the stopper sits too high or not high enough in the drain go under the sink with a flashlight and identify these parts per the illustration above.
Pushing the knob and the lift rod down causes the pivot rod to push the stopper up.
Pulling the knob causes the pivot rod to pull the stopper down.
Typically the putty seal around the flange keeps the tub from draining when the stopper is closed.
Your symptom indicate a faulty rubber gasket under the tub or a leak in a joint in the piping.
Not everyone knows that and often they think more is better.
You should be able to confirm that it is the drain that is leaking.
Lay a few pieces of paper on the floor under the pipes where you suspect the water is dripping have your helper remove the stopper while you shine a flashlight on the drain.
With a wide range of styles and finishes jacuzzi drain kits complete the look of your bathtub or shower and are offered in a variety of installation types from universal deep soak to the contemporary linear overflow.
Jacuzzi drain kits.
If your tub is leaking you should always start your search for the leak by checking the union fittings underneath the tub.
On some styles the rocker arm on the drain stopper fits between the coils on the spring.
So go into the basement or crawl space under the tub and check to make sure they are tight.
The vibrations in a jetted tub can cause union seals to shake loose and leak.
In these cases less is better.