Heck, I have that problem with my normal English-speaking employees.
The trick here is to use multiple communication paths.
First, don't rely on them to tell anyone else about your due dates etc. Say it's your job to tell people about things like that, especially your boss. Tell your boss "Hey, please don't take any of my guys' statement about a deliverable as a commitment, they don't always understand me, I will update you myself." If you are proactively communicating then the "telephone game" gets nipped in the bud.
Second, make sure there is at least one and ideally two other forms of communication about important items like deliverables you're all agreeing on in the team. Have an in person discussion, but then ideally also send an email and then put details in e.g. a ticketing/work tracking system. They may misunderstand in person, but if there's an email to the team saying "We are going to deliver this compliance report by Dec 17, and Joe said he is responsible for delivering it" and there's a ticket with a due date of "Dec 17" on it assigned to Joe, there's a lot of self-correcting opportunities.
Third, figure out how to clarify with them. Cultures are different; some are much more resistant to saying "no" or saying they don't understand or are more reluctant to ask for clarification. I've worked with Indian, Japanese, German, Spanish, and other kinds of employees and you have to do a little research on how best to communicate with each, it's different. Be patient, leave enough time in these discussions to get to a real understanding, and then use those techniques as well as basic communication techniques. Have them repeat back to you the expectation and if they need anything to meet that. Under no circumstances should you hear something a little off and just say "well, I'm sure he got it..." You have to make sure it's clear.