That's normally how it goes. At least, I've always had the background check happen after an offer is signed. It's usually a separate company and they just report back whether your job titles/employment dates match your resume

I don't know how common it actually is. I've always provided references and probably OKd a background check but post-school my few jobs have always been through people I knew and there was really no reason to run a check except fr pro-forma reasons.