38M and 32F gray area of cheeting

I've been dating a guy 38M for 3 months and we were very excited, we saw each other almost every day. 1 month ago we agreed to an exclusive relationship, because I 32F felt insecure that he was seeing other girls. However, last week there were some mishaps. He told me that at her work there was a girl interested in him, I asked him to please set the limits with her, and to be especially careful because in my previous relationships I had had very bad experiences regarding these issues. The thing is that 2 days after that conversation, he tells me that he went to a party with his co-workers and that he danced with her all night, closely and that they almost kissed her. I don't quite understand why he told me, but he told me that he regretted it, that he wouldn't do it again, and that he told me out of guilt and to try to be honest with me. Be that as it may, I am very distrustful of relating to someone like that, who, knowing that for me the triangulation of relationships hurts me, does the same, and precisely with the person we had talked about. To make matters worse, after that discussion, he offers me to start a formal relationship and being his gf so he can effectively be faithful with all the restrictions. I think he is manipulative on his part and I don't trust his intentions or strategies, what do you think?