There is a mile of downhill on my way to work every day. I oberseved that when I step on the brake to slow down, the RPM jumps from 2000 to 4000 all of a sudden and stay there for a few second. Without my foot on the brake, the tachometer stays around 2000 rpm. Is it normal? Why does the engine do this?

 

Could be tranny downshifting and using engine braking?

I'd try to put it to S mode and see if the same happens.

 

Not sure about the technical wording on it but it's supposed to do that. If you brake and going down hill it will downshift to help slow the vehicle down. If you then step on the gas it will again upshift. Had me freaked out when I first bought mine but I figured it out.

 

Yep, that is correct. Our 2004 did it and the 2013 does as well. Perfectly normal.