Over-the-phone order and UPS?

Okay, so I ordered a few things over the phone and they are shipping via UPS. So, whenever UPS receives the package, the company I ordered from notifies me via email that the items have shipped. However, I have not received any information on my items. The company says regularly-stocked items are shipped promptly, and I ordered regular-stocked items, and I was wondering, how long would it take UPS to receive billing information, and are the chances good of UPS receiving it tomorrow? Also, I have ground shipping.