This is not a first day cover. It is a first flight cover, but missing the cachet it should have.
Date difference: It was mailed and cancelled on the 30th as a normal cover would but would not have been carried/"despatched" via transatlantic clipper service which left on the 31st. Normal stuff, nothing special. You drop mail in the local box or post office, it gets cancelled there or the main PO and is sent onward. The Pan-Am Clipper didn't take off from Stoke-on-Trent, either. Postal workers would have paid attention to the endorsement "By North Atlantic Air Service" and the rate paid; there was no regular transatlantic airmail service until this flight.
Route: The writer is correct in the complete routing. Though there was a stop in Southampton UK that dropped off and took on mail. This cover is supposed to have a cachet. The position of the typewritten address may have prevented a clerk from applying it.
Reversed Stoke-on-Trent cancel: It is
an offset/set-off, but not from another cover. The cancelling machinery picked up the postmark, perhaps when an envelope got stuck. The reversed postmark then transferred to the back of this cover. The bars were transferred from another such event with the machinery. Covers are run through the cancel machinery upside down so there is nothing odd about the position. Commonly found.
the cachet for service from the UK, known in black also.