Regarding her boyfriend and her dad, is it possible that they did call the police? We know that the owners of Common Grounds called the police after reviewing the tape and at that point it turned in to an abduction, but before that call it's possible the police were notified and were only treating it as a possible missing person.
It wouldn't have even been twenty-four hours that she was missing at that point so the police might have figured that she just took off and would turn up on her own soon.
In this article, the owner of Common Grounds says: ""We didn't even have a red flag," Duncan said. "We didn't know anything was wrong until we found out she hadn't been heard from."
http://www.adn.com/2012/02/03/2298379/police-continue-search-for-missing.html
So it appears that they were alerted that she was missing, at which point they then reviewed the tape and saw that it was an abduction.
It could be that the police contacted Common Grounds after the victim's boyfriend or father filed a report. Or the boyfriend or father might have contacted Common Grounds on their own.
Either way, it does seem that they were concerned and likely took steps to find her before it was declared an abduction.