I just checked my own business page (I have an author page) and I agree, there doesn't seem to be a setting for auto-play, or to turn it off. At the same time, videos don't automatically play on my page.
Are these Vines or YouTube videos, or something you uploaded straight to Facebook, or something else? Are you seeing this on a desktop or laptop PC? On a Mac? On a phone or tablet, using a Facebook app? It's possible that the differences are stemming from either the content, or how it was shared, or the app or platform where you're accessing Facebook. I can't promise that any of these would fix the problem, I might add, but at least if you knew that the issue is only with videos you've uploaded directly, you could instead put them on YouTube and then just share YouTube links, that sort of thing could be a reasonable workaround.