Rest assured that you haven't stumbled upon a conspiracy to obfuscate the sultana's age for nefarious ends. After a brief discussion with Fern and Oda-san, we managed to clear things up.

First of all, this will be the revised text for the minion description:

Quote Originally Posted by Fernehalwes
This clockwork doll is a reproduction of a model first crafted in the year of the Calamity to celebrate the tenth anniversary of Nanamo Ul Namo's ascendance to the Ul'dahn throne. Seventeenth in her line, the sultana was crowned when she had seen but five summers.
To reiterate, the original model was crafted on the eve of the Calamity, and the player-obtainable model is a reproduction. Given her state of mind at the time, you can imagine that the sultana's feelings towards the doll were somewhat mixed.

So how did this happen? Well, Oda-san admits that the JP text is a tad vague, and Fern says he had a brain (eye?) fart when writing the EN. On behalf of them both, I apologize for the confusion.

Oh, and you may have noticed that the following line is not included in the revised text:

Quote Originally Posted by Fernehalwes
She is not, however, the youngest to have ruled the Jewel of the Desert.
Don't cry retcon just yet! We cut this only because there wasn't enough space. Feel free to continue speculating what poor child was forced to rule at an even younger age.