Hi,
Please try this:
Open that template, then go to Design tab -> Themes -> Select a theme, check if the theme is applied to the drawing.
(Since I don't have the "Illustrator", I'm sorry I can't do the test for you.)
If the theme can't be applied to the drawing, this thread should be discontinued here, which means we can't make it follow the theme colors.
If the theme is applied to the drawing, please note, the themes are not stored in the template itself. If you have a custom theme, it's stored in a .thmx file, and the location should be:
C:\Users\v-yadche\AppData\Roaming\Microsoft\Templates\Document Themes(Office 2013, Windows 8.1)
If other users don't have that custom .thmx file, they will need to have a copy of it, or make a custom theme by themselves.
If I misunderstood anything, please feel free to post back.
Regards,
Melon Chen
TechNet Community Support
