So if Tevruden only unconsciously has affectionate feelings towards her, he doesn’t recognize it as a relationship? Then is it simply a situation of her being handy in a fight that explains why he is around her?

Tevruden doesn’t really think about relationships in the first place. He knows that Feiyn has feelings for him, and he’s been asked about why he promised to protect her and hangs around her, and stated point blank that he doesn’t actually know why. He’s satisfied with that answer and nobody has gone and suggested he should go find out a reason either, so he probably isn’t going to.

He’s really a giant dork when it comes to social interaction.