I just had a quick look on my characters, and it seems like the completion date is only updated if you check with a character you re-did an achievement on.
If you didn’t re-do an account-wide achievement on a character, the date shown on the achievement is the original date you first earned the achievement on for the account, as well as which character gained the achievement. If you hover over the points in the specific achievement you want to check, it should say “First Earned by:…” followed by the date, and that the character you’re checking it on hasn’t completed this achievement themselves yet.
Just as an FYI, I didn’t check for the diplomat achievement specifically, but I see no reason why the behaviour would be different there.