I know dangerously little about Word on the Mac.
However, multilevel numbering is fussy.

Are your styles set up following the directions at How to create numbered headings or outline numbering in Ribbon Versions of Word by Shauna Kelly?

If so, try reattaching the template two more times with update styles. This last is pure guess. I know that when styles rely on each other in Windows it can take three copies using the Organizer to get a usable set of Styles.