Nothing to worry about, this is normal and most brands have it this way. Rolex has an instant date change but it also doesn't happen at midnight precisely and have be a couple of minutes off. Personally I prefer when it "slides" over to the next day.
Some additional advice, read the manual that came with the watch and follow the instructions when setting the date on your watch. Doing it incorrectly can damage the movement.
All things aside, congrats and enjoy the watch!
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