They show a shot of him right before the DS explodes. In movie grammar, this is indicating that he is onboard the DS a second before it blows up. The film was not structured like that originally, but the editors decided to intercut Tarkin to increase the threat and remind the viewers why the DS is being attacked, and also give bigger emotional payoff when it drives home that the main villain in charge just got destroyed.
It was very much intentional, and that's all there is to it. "Stand by, stand by", shot of X-wings flying away, shot of Tarkin ONBOARD THE DEATH STAR, cut to massive explosion as all perish. They added that shot just to remind people--hey, Tarkin didn't evacuate, he is still onboard counting on the Death Star firing first, and they almost do but then BOOM.
End of story.