Libraries and colour

Hi,

I'm new to using Adobe CC libraries. Here's my issue:

1. I've created a set of library colours to be used across InDesign and Illustrator.
2. I apply a colour from my library to a frame background in say InDesign.
3. Then, from Illustrator, I update this library colour - however the updated colour does not apply to the frame background in InDesign?

Maybe I am misunderstanding the function of libraries, but does the colours in CC library, not update the colours applied to objects in the apps using that library?

Thanks,

Alan