Tuan and Philip were not watching Cranes (the Russian song). They were watching The Fly (1958). I don't know if the film about a man who turns into a monster triggered Philip's flashback, or if it was the combination of Tim's diary and Philip feeling like he doesn't know his children, especially Henry. The music started when Philip arrived at the Ekert house, so I think it's something that was weighing on him before, hence his detachment with Tuan. But the monster aspect and the idea of change set up the theme of the episode. I thought Philip remembering a happy time with his father played into his reluctance to kill Natalie. His father did horrible things and presumably killed Soviet prisoners, but he loved his family. Philip does terrible things but wants to change. If you can't change and leave the past behind and become a better person, then what's the point? Should you be held accountable for following orders or doing things that you would never do now, is the thing I think Philip was asking Elizabeth, and that's all related to his flashbacks. I'm still super interested in Philip's flashbacks, and I really want to know about his father's death and what happened to his brother.
But I agree with the general sentiment about Tuan. I've been extremely interested in him and his story, but he and the Morozov family have been used almost exclusively as lenses for Philip and Elizabeth. They don't jump off the screen as interesting characters unto themselves like William, which is disappointing.