Is it normal that my fiance checks out girls profiles on sex sites and chats?

I'm wondering if I have a reason to be upset, hurt and to feel cheated on. My fiance and I have an understanding that as long as he tells me and I'm okay with the person, he can mess around with other women. I also ask that he tells me if he's going to go on things like chat roulette or omegle to try and manipulate with other women. Porn doesn't bother me at all, but what has and does is when he searches out specific girls, normal ones even within our area and comments and sexts with them without telling me at all. It makes me feel lied to and the fact he keeps it from me makes me feel like I'm not "good enough" anymore and these specific girls are. I'm not a jealous type usually, at least when I know what he's up to, but I went through his phone one night months ago ( simply because he does this to me all the time, he has trust issues with me for no reason except that I'm so okay with him being free to do all that stuff, but I don't even and wouldn't want to have or think about sex with anyone else unless it was a threesome) and when I went through his phone, I was upset by the people he was following and what he was saying and posting. When I asked about it, he freaked out on me and told me I was being hormonal and over reacting. After a huge fight about it, he agreed to not follow specific women or comment. The other night, I got curious again after realizing he was starting to act distant like he was the first time and only scrolled through his internet history a few days back and saw the same things he agreed to stop doing. It really hurts, especially that I was lied to. I haven't confronted him yet but I left to stay a few nights away. Do you think I have a reason to be upset? Should I try and do the same and let him find it to teach him a lesson?