I agree with the recent comments about how your relationship is otherwise. I'm so glad other people who know about this site have commented. I think the bigger question really is whether you are happy and fulfilled in this relationship. If you are both amazingly happy and in love, you can get past this with a fuller, deeper discussion and reestablishing boundaries.
I suspect that this is not the case?
How are you proceeding for the time being? Is he sleeping on your couch, or is he still slumming it in his flat below? Please don't just let him stay with you for convenience or out of pity. He's a grown man!
I think I would really dislike it and be uncomfortable with a partner being on a site like that. The reason being, if he had been exchanging messages or if there was any interactive stuff/porn. Porn in itself, I can accept so long as it's not frequent, it just seems like everyone looks at it. If I really trusted a partner and he says he was just curious, and that's the end of it, that would be fine.
The key element here is trust generally. You also said you had a feeling that something was off, which is why you looked. What gave you that feeling?
Btw, you have nothing to beat yourself up about!