Background checks are basically to confirm dates of employment and also whether there is any criminal record. I think it's illegal for an employer to share any ratings or reviews, with anybody else.
Also, since they only go through the trouble of doing a background check after they are ready to make an offer, meaning that you've done well in all the interviews, they'll never change their minds because of a bad rating at a previous employer, or even what your reason was for departing that employer. If they find out you lied, however, it may be a different story.
Bottom line, if you told the truth, and don't have a record, you have nothing to worry about.
Hope that helps,