A family of Microsoft word processing software products for creating web, email, and print documents.
This is nothing new in Word 2016. What you're witnessing is due to adding Captions to floating graphic objects, especially if more than one object is anchored to the same paragraph. As long as you're dealing with floating objects it will require taking some additional steps. It's compounded by the fact that the Captions for floating objects are added in Text Boxes which, also, are floating objects. Fields in text boxes do not update instantly & when you move things around sometimes the Caption becomes anchored to a different paragraph than the object to which it pertains.
The easiest way to update the numbering is to switch to another view (such as Draft) then back to Print Layout view. That usually will update the numbering - again having multiple objects anchored to the same paragraph will interfere with the updating because the program doesn't always know what the preferred sequence should be. To force the updating, click on the figure number then press the F9 key [fn+F9 on a laptop] to update the field manually.
Also, as Daniel pointed out, the fields will update when you print [if the Update fields box is checked in Word> Preferences - Print] as well as when the document is reopened. (Actually, you don't have to print the document - just going to File> Print then Cancelling usually is enough.)
To keep the Caption text boxes with the graphic, select both the object & its Caption, then apply the Group command.