I've been cruising since I was 5 years old with Celebrity. Always had my own Captain's Club number, so when I was over 18, all I had to do was associate it with an email and I could manage my own account.
The only thing I had to do was submit proof that I went on the same cruises my parents did. When I started cruising back in the 90's, records for the kids weren't really well-kept, especially with promotions like "Kids Sail Free", etc. When I associated my number with my email and noticed some cruises were missing, I had to submit the proof (old key cards, photos, etc.) so that they could see I was there and get me the credit I deserved.
Now my parents and I still have different point amounts, but we're all still on the same tier (we weren't before I submitted proof)