The trouble with been in a long term relationship, is that everything becomes old. You have the same old sex, the same old conversations, you know everything about each other, and so on. Suddenly a new person comes into his life, and yes, he's probably going to be interested. Now it doesn't mean he has romantic feelings towards her, he could genuinely be sick of the recycled conversations you both have, and as I said, this will be new and exciting for him. However, the personalized ringtone is probably so he can recognize when she's calling when his phone isn't in his presence, so he can answer it, which is honestly unsettling along with her photo been used as caller ID. This makes me think it's a little more then something new and exciting. Now there's nothing to suggest he's cheating or fucking her, but he's definitely up to no good emotionally, often people refer to it as emotionally cheating. And it's more likely to occur with people with long term partners. The fact you told him this is wrong and makes you uncomfortable and he still does it regardless is the most worrying bit. Relationships are about compromise. And he's not willing.
I would sit down and talk, discuss it. Lay everything on the table. See what the real reason is. Perhaps if it's your relationship, you could either forgive him and work together and fix it, and if you can't forgive him, make ammends or go seperate ways. I'm sorry you're going through this, I understand it's annoying to go through this with somebody you've dedicated your life with.
I'm going to be honest and say I did this when I was with my ex-girlfriend. She was boring in every way, but I had feelings for her. I never flirted or cheated or even emotionally cheated, but I just lost interest in her and gained more in other people. I know why people do it, and it's a horrible thing to honestly do. To avoid this happening again, and common reasons why this happens is;
But this is just advice, it depends how badly he's fucked up here. You have every right to be worried, and I'm all on your side aside from looking through his phone. You should be worried, this needs resolving. It's up to you to forgive him and try fix it, WITH HIM. Don't read this and think I'm expecting you to fix it all, he has to fix the majority of this.