@S 1992,
Maybe I'm wrong since I don't use my phone to browse the internet very much, but I have never had a website just pop up on my phone. And even if I did, I would not call the site and start a sexual conversation with some random woman. And you say you heard him making plans to see her?
I think you have every right to be upset at him. I would keep a very close eye on him because it sure looks like he is at the very least entertaining the thought of cheating.