It has not been announced whether they have a match or not.
The latest I read (from AP) says they did a mouth swab for DNA on Karr yesterday and will get more samples once he returns to the U.S. That tells me that the "DNA match" report from yesterday is at best premature. Why test the guy twice more if you already have a match?
I think the prof tipped off the police. The police found him in a foreign country, considered him elusive and a flight risk (he skipped the kiddie porn sentencing in Cali) and swooped in while they had the chance - not because they had solid evidence to convict but because the opportunity was there to get him at that time. Only now can they start building a case against Karr.