We're in the pov of AFO talking with his dad. Implying the Decay quirk was given to Shigaraki from him.
Honestly it's always been a given that AfO was directly involved in what happened. The guy has a massive boner for anything remotely tied to OfA, and it makes perfect sense that he would go after Nana's family. Hell, in one of the chapters before he died it was mentioned that in the past he would hunt down and kill relatives and loved ones of previous holders, effectively ending any chance of their bloodlines continuing.
Now you have Tenko and his family, with him just so happening to develop an extremely dangerous and unstable power which his body isn't able to handle, like what we've seen of other characters in the series that received quirks their bodies weren't compatible with. Then things with Tenko go out of control, with him killing his entire family, and AfO just happened to be there to take him under his wing.
One interesting question though is does this mean that Shigaraki was originally quirkless like Deku, or maybe he had already had one. It could be a case where whatever he had was modified by that one doctor, or just switched out by AfO. More interesting though would be if Shigaraki actually did have a second quirk, which would explain a lot. It was stated that possessing one or more quirks can greatly effect ones body and shorten their life, and in the case of Tenko/Shigaraki it would explain how's always been shown scratching himself and being mentally unstable, even back when he was a kid, something I feel only got worse the older he got.