water pressure regulator releasing a tiny bit of water

Normally these are non reliving so no water leaks when the pressure changes, this may cause your pressure to shift a few psi on occasion but not more than a few psi.

I am wondering if you got a reliving type regulator. These regulators release the over pressure ( normally caused by water heaters) the pressure is vented thus the leak. Most of the time a pressure tank is used to absorb the pressure created by the water heater and a non reliving regulator is used. If you purchased a reliving type you don’t need a pressure tank but it allows some water to be leaked out to maintain the pressure.

This is if the water is coming from the regulator from the looks it might be condensation.