Yes it's normal. What if your bf and his ex just wants to be friends? Is it wrong for friends to check up on each other??
I believe calling his ex to see if she is okay is a legit reason and nothing to worry about.
Get back with him, he didn't deserve what you did to him and I strongly believe he needs a second chance, so give it to him.
But be on your toes, if anything seems fishy, than ask him and talk to him. Let him explain the best he can. Basically be understanding.
In my opinion, what you did was unfair, breaking up with him over such matters.
Give him a chance, he might be actually checking up on her like he said and you might look stupid thinking that he was going to or is cheating on you.
Remember in most relationships, guys worry more about the possibility that his girl might break up with him, no matter how stable the relationship is.
Tell me what happens.
Cheers,
Peter