Hey there D3f_u,
Thanks for reaching out!
You mentioned using Family Sharing, so we want to check:
- Make sure you do not have the same Apple ID set up on both devices where the profile photo is being changed. This can cause information to be shared, like the photo, when sharing an Apple ID.
If the other person sees your photo change in Messages, it's likely you are sharing the name and photo for them to update when you update your info. Use this link to check: Share your name and photo in Messages on Mac - Apple Support
When you say you change their profile picture in messages, are you also using the steps from the link above? Also, is the other contact making any photos around the time you are, or possibly after you changed yours?
Reply with more details for additional help.
All the best.