Would you consider this cheating?

My boyfriend used to work at a retail store. All his employees were female but there was one in particular I had a problem with. At the time she was a high schooler and he was a sophomore in college. He had a class project where he had to observe a high schoolers day to day life and emotional and mental stability (He was a human development major). So because of this they started to spend a lot of time together (During this time we lived in different towns 2 hours away from eachother so we barely saw eachother.) One day he texts me and says he was up all night trying to calm her down because she texted him at 1am saying she had a nightmare 🙄 I got upset and said no girl would text a guy for something like that unless she liked him. He of course didn't believe me and said they were just friends and continued to talk to her late at night. He stopped telling me about it though. So fast forward a month later, I moved down to live with him. We had it planned out for awhile but when I moved in with him everything started to unravel. One night I wake up at 2am and see that he is texting. I ask who he is and he says NOBODY. Then his notification goes off and what do you know? IT'S HER. I ask to see his phone and he nervously laughs and says no and I continue to ask until he gives it to me. I read their messages and my blood boils. She was calling him "bae" and talking about how much he comforts her yada yada. So I go off on him and ask how long he's been texting her like this and he tells me she told him a week ago that she likes him WHICH I WAS RIGHT ABOUT AND HE GOT MAD AT ME FOR SAYING and he still continued to talk to her even though he turned her down because he was dating me! I told him I did not want him talking to her anymore if we were going to stay together because all of this made me uncomfortable. He agreed and said he wouldn't talk to her anymore. WELL the next week guess who wakes up to him texting her. Yup. And he says she was the one texting him and he felt bad for ignoring her. At this point I was done. He begged me to stay and says this time he would stop and blocked her number. Keep in mind they still work together and he is a supervisor so he still talks to her. Everytime I went into his work she'd be around him flirting with him and gave me the dirtiest look. She also spread rumors to all his coworkers so everyone there hated me. Months later he finally quit working there and I thought we were finally free of this girl but no. I'd catch him talking to her in the store like nothing was wrong. At this point in time he knew I hated this girl and hated when he talked to her even though he agreed not to. We went through so much fighting because of her. I finally put my foot down and said enough is enough. He needs to stop talking to her if he wants our relationship to go back to "normal." She eventually got a new job and everytime she did my BF magically knew about it 🙄 About a year later we both work in the same mall. We were texting and then suddenly he stopped replying. He was at work so I said whatever and was going on my lunch. As I'm walking I pass by the store where she works and hear her giggling. I never walk by that store because I hate having to see her but her giggle made me roll my eyes because it was a flirty giggle. So I look up and can you guess who's there talking to her? My boyfriend. Something in me snaps and I text him. He checks his phone, sees my text but doesn't respond 🙃 So I call him. He answers. I ask him what he's doing and he says he's getting a water and I say oh really? I can see you and he goes quiet and I just say are you serious? And he's like what we are just talking so I hang up on him and go back to work. We get into a huge argument because he says he was just saying hi but he knows that I'm uncomfortable with him talking to her and that we have almost broken up many times because of her. I don't know what it is but he always finds his way back to her. he just can't not talk to her. We eventually moved states because I decided to forgive and forget but it still bothers me. Whenever I think about it I get so mad. If I bring it up he gets upset and says he is tired of me talking about it but I just feel like it was wrong so I'm trying to seek advice now. Am I really overreacting or was this a type of cheating? it wasn't physical but emotionally it felt like it.

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