TL;DR: The distribution of the characters responds to the proximity of the upper keys to the finger and the frequency of use of the characters.
I think it is because of the way the iOS keyboards organize the keys. Take a look at this screenshots of the keyboard:
On the iPhone when you press the key, all possible values go to the list. This probably is due to the small size of the screen which makes the finger be covering the whole character.
On the iPad the main character stays in its place while pressing the key.
Now, I think there is a distribution that responds to the proximity of the upper keys to the finger and the importance, or frequency of use, of the characters. The closer to the finger the more important (or more frequent) the character. [In the image the numbers represent closest key to the finger holding, 1 is the closest]
The closest character in each list is located on top of the finger on iPhone and below the finger (in the same place?) on iPad (after the first character iPad follows iPhone's order). Then the one on the right (my guess is it might be easier for right-handed) then on the left, then on the right, etc.
and then if there are more characters it goes to the upper row and continue from the center.
You can notice that this rule is also consistent with ? ¿ or ! ¡ which are displayed reverse way.
If you look close to the distribution of the characters you are asking about, on the iPhone they are distributed the "correct" way (left on the left right on the right):
but it is just a matter of coincidence.
On the iPad each character has the same order (proximity to the finger importance) which makes the right quotation be on the left (by the way, the character 1 represented in the keyboard is not the actual character):
Why would the right character be more important than the left one?
My guess is it might be more frequent. Here is a link which might prove some uses of the right character by itself.
And about the right double quotation, either it is more frequent than the left one or, as @Crissov stated in the other answer, it follows the single quotation order.