Am I to Blame?

My ex and I were together for almost 5 years (we also have 2.5 year old twins) and he cheated on me way too many times and I was dumb to keep running back to him. Just a couple months ago, I learned that he was cheating on me with a girl from the church we went to (for almost 7-8 months). He didn’t tell her we were broken up and he would never communicate with me. Then a couple weeks ago, when things got tough between us he ran back to her. I could’ve went off on her but I chose to be civil about it. That being said, I messaged her on Facebook last night saying “hey! It’s been a long time since we’ve talked!” And exchanged 2 friendly messages after that but then I decided to stop. Ever since then, her and my ex have been discussing why I messaged her in the first place. The girl came to a conclusion that she needs to rethink their relationship and what they’re doing.

My ex BARGED into my room yelling, calling me names, and accusing me of ruining their relationship because I talked to her. When I tried to ask him what I did wrong that caused this sudden accusation, he continued blaming me and what not.

Is he right to blame me for her second thinking and potentially ending their “relationship”?