I just tried this on my new (2 month's old green dial AT) and noticed that the minute hand did move slightly when pushing the crown back in. Now, with that said, my observation is that it moves to the range between the minutes based on the second hand's orientation. For example, if the second hand is at 30 seconds, the minute hand would be right in the middle of the minutes (50% to the next minute).
Give that a go!
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