Converting ai files to be printed from coraldraw

Does anyone have any advise how to improve some colour issues between programs? 

I use Adobe ai cc 2015 to produce artwork to be printed in china, where they use coraldraw.  Unfortunately 2 different factories are having the same problem, when they convert the files, all the colours become too vivid, especially the orange & purples are too bright. Is there anythink I could do to prevent this or is there anything I could suggest to them?   thanks