Fishing for conversation?

Brittany
This is about my sister but her husband looks on her phone so she asked me to post it. Anyways, her DH has a 2 year old from a previous relationship that he's just learning about. My sis is thrilled and is encouraging his involvement in the child's life! Honestly I think she's being pretty great about it. She trusts her man too. His ex however, has been messaging him about their child which is completely fine with her but she thinks they may be crossing a line. She doesn't wanna say anything to him because she doesn't want to discourage him in any way, but his ex is constantly sending smiley faces. She is being overly friendly to him. Telling him she hopes his marriage is happy and full out of nowhere. He asked her for pics of the baby and she sent him a pic of her and the baby and then just an hr ago at 10:30 at night she messaged and said "hope your day was well". I am biased so I can't have any input but my sister wants to hear that she is just overreacting to something stupid but wants to know if his ex is fishing for more conversation? I personally think she is but other opinions are welcome!