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Yes that is perfectly fine. Watches change their dates over a given period, not necessarily on the dot at 12 midnight.
Here's an explanation from Chronocentric with an uplifting final paragraph to allay your concerns
There are two major ways a mechanical date window changes on a watch. So the answer to this question depends on which type you have. This applies to any watch, mechanical, automatic or quartz, where the date window is implemented as a mechanical function instead of an electronic display.
Watches with slow date change have the date roll over very slowly. Sometimes these watches may take one to four hours for the date to completely roll over. This is perfectly normal for many watches. Though it can be confusing if you are awake between 11:00 PM and 3:00 AM and want to be certain what date it is.
Watches with rapid change date have the date window rollover very fast--often within a fraction of a second. This is a more precise way of displaying the date, but requires a more complicated mechanism. Having the precise time that this rapid change occurs be off from midnight is a common issue. Rapid date change watches usually come from the factory set for the date change to within 10 minutes of midnight. But it is not unusual for this to get further out of adjustment over time from one of several causes.
It is possible that a shock to the watch right around the date change can throw the mechanism off. The more common causes are from the owner manually changing the date within three or four hours either side of midnight, or setting the time backwards across midnight. The frequency that this problem occurs makes it disconcerting that few watch makers provide warnings about this in their instruction manuals. What happens is that if you alter the date setting while the date change gear is near to pushing the date forward, you may push the mechanism slightly out of alignment. This seldom causes any real damage, though it can. Most often, it will shift the time that the date change occurs--usually further from midnight.
The good news is that this is easily corrected when the watch is being serviced. Simply mention the date change is off when you send the watch in for its routine cleaning or other service.
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