In my experience in the US, it's normal to check references before extending an offer. You might be wondering why they don't make the offer contingent on the reference check, like they usually do on a background check, but there's an important difference: the reference check is under their control and usually quick. A background check, on the other hand, can take weeks.
So given a choice between saying "yes" today and then having to have the awkward "um, no, we learned something" conversation tomorrow, and just waiting until tomorrow so they can do the check first, most employers will do the latter.
In a hot market or for a super candidate, an employer might choose to do it the other way. But from what I've seen, they'll instead say "we intend to make you an offer and are just checking references now". If the references don't pan out there's still an awkward conversation, but they don't have to retract a formal offer.