Your problem is caused by the fact that the watch is 12 hours out of step.
Wind your watch forward 12 hours, reset the date if you need to and you watch will then change around midnight.
(if you need to change the date more than one day, when it has past the change time, wind it back and then forward to step the date forward. You may have to experiment to see how far past the change point (in both directions).
Answers & Comments
Your problem is caused by the fact that the watch is 12 hours out of step.
Wind your watch forward 12 hours, reset the date if you need to and you watch will then change around midnight.
(if you need to change the date more than one day, when it has past the change time, wind it back and then forward to step the date forward. You may have to experiment to see how far past the change point (in both directions).