Do you have a dog?
I say this, because I have 4 cats, One was an adult when we got her, and does not do this.
The other 3 were kittens, and all have been mothered by my dog, and wag their tails, when you talk to them, or fuss them, in the same circumstance as a dog would, but, being cats they do wag differently.
(One of them barks with a miow when you knock on the door)
Cat tails can shop emotion as a sweeping wag from the base similar to a windscreen wiper is generally a happy wag. If the tail is stiff and straight up, and sort of shakes a small bit that is more angry, or about to pounce. If the tail is floppy and the end moves, it is just dreaming and content.
I would not worry, just enjoy.
(Unless like mine it bashed you in the face with such a vigorous wag, cat being friendly but it still can hurt)