this sink type is not uncommon, but I've never had one quite like this......
first, the faucet in the picture is in that position so it can be rotated between either sink for use......as opposed to the faucet you have, you said, which you said is well to the right......
I do wonder why the disposal is in the small sink rather than the large one, as you said it is.....I would've guessed the small sink is primarily for washing vegetables/fruit and the large sink is for dish washing and, thus, would have the disposal.....