Hello Timmy. Yes, you have it right, it is called a chin mudra. I have come across different interpretations how exactly is a chin mudra performed. Some authors say it is done with the tip of thumb and index fingers touching and they call the variation where the index finger is folded under the thumb gyana mudra.
But I have found also read that both are done with the index finger folded under the thumb, but in chin mudra the palms face up and in gyana mudra the palms face down.

I personally wouldn't worry too much about "a correct version" and do the variation that works for you.
The mudra is done to form a circuit between the thumb and the index finger to direct the energy that would normally dissipate out of the fingers to the environment back to the body and up to the brain.
As it works on the subtle energetic level, you can't really tell from the outside whether it is working or not. But in a deep meditation, you might feel it does. However, when you just start practicing yoga, there is no need for you to worry about feeling any such effects, just keep practicing it and eventually it will come.

Hope it helps.