You could start by not calling out and generalizing an entire continent's worth of cultures as shy, but...to your question...
Share more about your use case perhaps? Without knowing the function of your breakout rooms, duration and audience (aside from some of them being Asian), it's hard to give specific guidance. However...
Be sure to give clear directions and warn them of a report back. Have the groups designate a reporter that will speak to the findings of the group when the breakout rooms are over. Take time to discuss the purpose of having the breakout conversation before and after. Tease out the important learning in the process (which implies they are absolutely purposeful, of course). Provide clear expectations of the purpose, duration and what happens when they return (and if they FAIL!!! MWAUAHAHA! I'm obviously kidding - this never fails). Make your instructions crystal clear and use some sort of memorable guide posts for forgetful people like a number of things or an acronym - or share the instructions in chat which will follow them to the breakout room.
Here's an example based off of an inclusion/diversity training we are managing:
Sample Instructions: "We're going to move you into breakout rooms in just a moment and there you will speak with about 10-15 of your colleagues and fellow participants. You will have just 3 minutes while you are there to find 3 things that you all have in common. That's it. Chat to us real fast if you have an questions. Just three things that you all either like to do, don't like to do, are, eat. What you can't say is that you all work for ____ or some other thing obvious. Maybe get a bit personal if you don't mind. Maybe you are all married or all single. Maybe all play sports. You decide. So, 10-15 people, you have 3 minutes to decide on 3 things you all share in common with one another. When we come back, we will share what you discovered in chat (or verbal depending on audience size). That's it. 3 things that your group has in common that everyone agrees on. Ready? Here we go"
Hope that helps you out some. Feel free to reach out to follow up. I check back here occasionally,.