I like too think in the first two Gifs, he didn’t stumble upon her by accident. He chose to go after her. No one told him to go and save her, he went on his own.
He always protected her in his own way.
Protected her from Joffrey. Stopped her from killing him, knowing it would also result in her death. He stood up for her when she questioned him. He offered to take her away and keep her safe. He didn’t have to do that. He had branded himself a traitor, he should of left straight away, but he didn’t. He went to her room. He couldn’t leave her behind for Stannis or Joffrey.
She was his little bird.