By the end of first section, it becomes clear that Nanni and Paul’s father are engaged in a relationship, not Nanni and his own father. When Paul discovers their relationship he isn't jealous as we'd expect but happy.
From the text:
I was so intrigued by this person whom I was hearing for the first time that I stood on the threshold of the living room without walking in, fearing that the least step would interrupt the conversation. I wanted him to keep talking. Why didn’t he speak like this when he was with me? He was drinking something with my parents and was sitting in an armchair leaning forward toward my father, both elbows resting on his thighs, as though he hadn't finished his admission and was still imploring my parents’ leave to hear him out. When he put down his glass, I had the impression that he was just about to reach out and clasp one of my father’s hands. “I am the last person to give advice,” my father finally said. pg. 46
My father walked him to the door while my mother stayed in the living room staring at the desk. I was sure my father had stepped aside to pay Nanni’s fee, which is why I didn’t accompany him. As my father did with everyone, he walked Nanni to the end of the garden, opened the gate for him, and then stood there, courteous as ever, watching his guest make his way back toward the marina. Nanni turned back and waved a second time. No one had extinguished the candles yet. It made me think he was still in the room with us. pg. 48
My father’s admiration, unlike mine, was devoid of equivocation. I envied the absence of smokescreens and double-talk in what he’d said. Nothing stealthy or dissimulated about voicing one’s admiration for another man. Indeed, his praise of Nanni was so unhindered that it made me realize I had never said nor would ever be able to say anything of the sort. I’d have made up something crass about him or pointed to a birth defect here, a tremor there, if only to censor anything that betrayed what I felt each time | found the courage to look in his eyes. pg. 49
And those nightwalks with my father—he, like me, craving to run into Nanni and hoping that by extending our walks and making up excuses to delay heading back home, we might in the end run into him at the caffé. I was like a lover who is suddenly able to cobble together facts and realizes he’s been cheated on for weeks, months, or even years on end. pg 75
As I walked after dropping off my tutor in the early afternoon, I imagined the two of them on the very evening after our departure, having a quick meal together in the kitchen. A feast on leftovers. By then my father would have sent away all the help, and he and Nanni would be alone in the house, possibly listening to Beethoven as they sat on the veranda without candles or kerosene lamps, to avoid mosquitoes and prying eyes. Their days, their hours were numbered, and they knew it. San Giustiniano would not stand them much longer. Surely there’d been signs, threats, who knows. pg. 76
He might even be a touch amused—like father, like son, he says. “He’s been courting me for weeks,” says Nanni, “and the strange thing is that he probably has no idea. I don’t think he knows anything.” pg. 77
In the picture Nanni and my father are standing in bathing suits with the sea behind them. Nanni’s right arm is resting on my father’s shoulders, while his other hand is holding my father’s left shoulder. My father, his arms crossed, is smiling broadly, and so is Nanni, both trim and athletic. pg. 79
