Mobile is not my forte, so I’d be in uncharted territory with any type of suggestion. Does it happen in all mobile browsers? Is it just the PC responsive design you’re using or the other options? This could help explain the potential differences. I did a quick Google search and found a couple of articles that call out iOS that might lead to inspiration for the more savvy coders.
Optimizing Web Content (Apple’s developer site)
How to configure mobile Safari… (Talks about conditional CSS)
My initial guess is that you’ll need to adjust the CSS for different views, since the width and positioning of a video for mobile browsers is likely to be different than that on a PC.