I would definitely keep it to myself if it's something like first steps or first word. When I had my son in daycare, he did take his first steps at daycare and my provider told me about it and I really did feel I had missed out. I wondered why she had told me, but I know that she didn't do it maliciously...she just wanted to share and didn't realize how sad it made me feel that I had missed it and would likely miss a lot more by having to leave him to go to work. I guess that's why I have my own daycare now! So, as a provider, I do not want anyone to feel sad about missing a big milestone. However, if it's a new word they learned at daycare (not a first word) or something like that, I like to share so parents know the child is learning with me.