Does auto body buffer swirl remover work?

My car had some minor body work done in one area. I got it into parking lot lights and discovered the shop put some buffer swirls into the paint where they buffed out the spot they did the work on. You can't really spot them in sunlight, it takes direct parking lot style light to find them.

I took the car back to the shop this morning and the guy walked out to the car with a bottle of something and a rag, squeezed this tan looking stuff onto the spot and rubbed with the rag for a few seconds. I asked him what he put on it and he said it was swirl remover. I then asked if this was going to be a permanent fix or just temporary (cause I read you have to buff it out with an orbital buffer and some polish). He said it should be permanent. Is he lying to me? What I read about these makes it out to be a bit more involved than rubbing some stuff on the hood. I asked if I needed to wax that area now, and he said no. I don't know how something that's not abrasive enough to remove wax would fix the swirls.

Second question, assuming these swirls are still there, will they eventually go away over time with washes and waxes? They have to be really fine scratches that these things are comprised of, and surely paint wear would eventually rub them away.

Thanks!

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