Visable
PR and visible backlinks are only updated once every 3 to 6 weeks. But the benefit of inbound links and
PR may be seen immediately in the SERPs once a new inbound link is found, maybe not; there seems to be some debate about this.
Google does not show all backward links when checked, only a sample.
So an increase of 2000% suggests that no one was going to that site and now they are getting loads of traffic.
This traffic does not necessarily have to come from a SE. They could have been featured on "Good Morning America", launched a large ad campaign, or bought a fortune in AdWords, who knows.
Also Alexa rankings are notorious for their ability to be manipulated. You can't put too much faith in their results.