how water cylinder + leaking overflow + dripping not flowing
I have to say, similar to what @Grant said in comments, that an overflow valve is not supposed to have a normal drip. In normal usage your drip/overflow line should be bone dry.

The plumber that tried to tell you that a drip is normal is not to be believed. It is also likely that the plumber was far from professional if they just said that to cover up noting the drip right after the installation.

The pressure relief valve is a safety device designed to keep the hot water tank from exploding if the internal pressure builds up too high due to the heating source failing in an always on state.