Doubtful. They don’t show Vader ever going down to Tatooine in “A New Hope”, and we know he hates sand, so he probably wasn’t in any mood to visit. I think it was just the Storm Troopers.
Plus, if Vader had gone down to the planet, he probably would have sensed Obiwan was nearby, like he did when Obiwan was on the Death Star. So that also weighs against Vader being responsible.
You are correct. It wasn’t Darth Vader, but stormtroopers who killed Uncle Owen and Aunt Beru, the guardians of Luke Skywalker.