cancelled subscription, subscriber still has access

Maybe I'm a little premature here...but:

Client subscribed to a one-month recurring plan on May 1st. They cancelled on May 15th. It's June 2nd today and they still have an active enabled subscription with full access..?

Shouldn't the access have changed from Author to Registered by now? Or do I need to set up some sort of chron job to make that happen?

Thanks,
A