COLORS ARE ALL WRONG importing from Illustrator

Hey everyone. Sometimes when I import or open a file in Corel that was made in Illustrator, the colors are way off. It sometimes works to make sure the file is saved as RGB in Illustrator's Color Mode, but that doesn't work every time.

Here's an example, it is supposed to look more dull, like the pic on the right but in Corel it comes in bright neons.. :-/

I've had this issue for years. Currently using X7.

Thanks for your help!!