Reading other people's messages. Who is in the wrong here? Me or her?

My sister lives with her ex until she finds a place. Theyve been broken up months and months. He recently starts seeing a girl as a friend and she finds comfort in reading every msg he has with this girl. She eventually found something she didn't like and yelled at him for it, so he put a password on his computer. She gets in every time he forgets to lock it and eventually found a way around that all together and reads them through another device which he didn't realise had his password for Facebook saved.

I told him to change all his passwords and log out of devices just incase, but without outright saying my sister is in your business again. So he does. Then she gets his phone when he's in the shower. Now his phone has messages from me in there saying she's lost her mind and to change his passwords etc.

Now I love my sister--but she feels betrayed by me to have told him. Should my duty have been to my sister (and yes I told her a thousand times what she was doing was wrong but she didn't care and felt justified). Or was I right to tell her ex to lock his stuff up? I wasn't exactly saying lovely things about my sister to him because I really believe her behavior was crazy. But to say that to her ex is uncool....Is she totally justified in being angry at me for telling him? (he was a friend of mine before they were together, and I don't think he's a close friend at all, but he's close to my partner still)