Advice on Birth Parents & Facebook

Hello! This is my first post having just joined the forum today, mostly due to the fact that I would like some feedback on topics related to my semi-open adoption. For some background, my daughter recently turned one year old and I have been keeping touch with her birth parents through letters and pictures, which is all we plan to ever do - no visits. I met the birth parents a few times before the birth and was there for the birth (I even got to cut the cord and hold the baby first). I really couldn't have asked for a more smooth and ideal adoption experience. I decided to seek out some advice after talking with some friends and family. So basically, I have a Facebook account that I keep very private and share only with family and close friends. The other day, on a whim, I decided to see if the birth parents had accounts. I found them both the bf's account is private, but birthmom's was not. I was a little taken aback because her communication style is like a completely different person than her communication style was in person and is in letters to me. It sounds as though she is living a much faster lifestyle, partying, etc. rather than the low-key college student focusing on improving her life that she indicates in letters. She had posted pictures of the pictures that I sent her of my daughter (which is fine, but I would prefer her account were private if she is going to post pictures, I even made my mother change her account settings because of this-although it would have been nice if she would have asked me first). She also uses my daughter's birth name in her posts when she had told me that they were referring to her by the name I gave her, and made some other comments that would lead the reader to believe that she is parenting my daughter. I guess what I֒m wondering is if this is a common coping technique for birth parents, and if this type of thing should cause me any concern. I know shes still entitled to be a proud parent despite making an adoption plan for her baby, I guess I just donҒt want that line to be blurred in her mind. Ive never felt uneasy with the birth parents being in a nearby town because of our positive interactions and their assurances that they are committed to the adoption process, both at the birth and in letters; and while IҒve tried to explain it to family and friends, they are always a little bit concerned by the situation, particularly now. I told them that I had no plans to limit my communications with the birth parents because of this, mostly because they have done absolutely nothing that is intrusive to my daughter and I, and I gave them my word that I would keep in touch. I also think it will be important for my daughter to see that we have had open communication because I fully expect that she will be involved in the communications someday by writing letters herself. I would also be worried that if I did limit my communications, that may make them wonder even more about my daughter and potentially seek her out. I know that rarely happens, and I have told myself this when I find myself getting dragged into the alarmist state of mind that those around me seem to have sometimes, but I just really wanted to see what some other opinions were on the situation as well. Any insight you might have would be much appreciated!