When an order is marked as shipped in Monsoon the time that is sent for the order will be in your local time zone. The ship date that Amazon displays for an order is in Pacific time. Therefore, if the date and time that you marked an order as shipped will translate to a time that is before midnight of that day in Pacific time the date displayed on Amazon will be the previous day.
On the Orders tab, when marking an order as shipped, the time sent will be the current time if it is today's date. If using a previous day's date, the time will be sent as midnight local time.
Orders updated via a Data Exchange will use the time provided when setting the order to Shipped status. If no time is provided the time will be set as midnight.