Is it possible to change an adult account to a child one?
I had the same issue, I added my kids to Family Sharing but they showed up as adults (and so could make purchases without my permission). Fortunately you can easily change it. 

If you go to https://appleid.apple.com and login using their account details, in the Password and Security section, you can change the year of their birth. 1/1/2001 works fine, I think the key is that they need to be over 13 to change from Adult to Child account. I left my kids' birthdays with the correct day and month but used 2001. 

Going back to the iCloud section on my phone, it shows my kids as "Age 13".