It would be easier to diagnose the issue with a copy of the document.

Display non printing characters. How many appear on the second page?

Does the document use default or custom styles? If default then it's possible that there is a slight difference in the default styles between 2010 and 2016, one that results in slightly different line spacing--if there is just one or two lines on the second page, that seems likely.

If possible, post a copy of the template, please.