Please tell me I'm not crazy...

Okay, so my boyfriend and I just moved into a house together, and last night his ex texted him to say congratulations. Normally this wouldn't be an issue. Except this girl cheated on him, so I already know she isn't trust worthy. But even more than that, she can't seem to just move on. 
He unfollowed her on all social media after they broke up, but she still seems to always know what's going on in his life. She still obviously checks his profiles, because I recently got a friend request from her. I assumed it was just a mistake and left it alone. But she never deleted it until I messaged her, asking why she wanted to follow me. (I've never met her. I didn't meet my bf until I moved to the town I'm in now.)
She also still calls him to catch up and tell him her problems. Like when she thought she was pregnant with her new boyfriend (who she cheated on my bf with), she called my bf to vent. 
Is it completely unreasonable that I don't trust this girl or want her contacting my bf? He swears he's over her, but something just doesn't seem right.