Yeah, but....it's Putin. Even if it weren't, it's kinda 101 for your opponent to go after your family if he can't get to you.
If this was for real, I don't understand why he even took the deal. I expected if Prigozhin was going to revolt, he was fine with all or nothing. He already went traitor on the guy who windows people all the time for less. You don't regain anyone's respect after that even in normal circumstances, so I would have thought he'd really have nothing to gain and everything to lose from standing down.