Good question. A similar query applies to LBW. Does the off and leg sides get switched in regards to applying the different rules on LBW for the different sides? It takes some digging through different parts of the Laws of Cricket to get a answer.
The only thing I can find the defines the moment in time that the off and leg sides get defined is in Law 36 regarding LBW. It states
3. Off side of wicket
The off side of the striker’s wicket shall be determined by the striker’s stance
at the moment the ball comes into play for that delivery.
So when does the ball come into play? If we go to Law 23 we find
5. Ball ceases to be dead
The ball ceases to be dead - that is, it comes into play - when the bowler starts
his run up or, if he has no run up, his bowling action.
This means that the original definition of the sides stand, so this won't be called a wide. Note that there may be some additional clarifications about this in the playing conditions, but I couldn't find anything.
I know that in the case of LBW this is true; the original sides stand. I know this because many people have suggested, correctly in my view, that the laws should be changed on this point.