References Called After A Job Offer?

^{I accepted a position a couple of weeks ago, and filled out some paperwork and went in for my drug test. I haven't met with HR, but talked to her on the phone...she said we could wait on the rest of it, since I won't graduate for a few weeks. I just got an email from a professor letting me know that she got a call, as one of my references...Is this normal? Wouldn't they check the references before offering me a job? I'm getting nervous, now, that the job will fall through (for whatever reason!)}
It's pretty much the norm for employers to check references and criminal background before making a formal offer, especially in healthcare.

That's what I was thinking. They offered me the job and I accepted, but maybe it's not a "formal" offer until after my background check and drug test come back clean? I just assumed that they would have checked my references before they made a job offer at all. Thanks for your quick reply! I really appreciate it.