How does national law work internationally.

and see http://www.fas.org/sgp/crs/misc/94-166.pdf

As others have indicated, extradition is a creature of treaty. Most extradition treaties require double criminality. International Criminal Law - Ilias Bantekas, Susan Nash - Google Books

So extradition and criminal jurisdiction are not coterminous.

To the OP: It’s important to distinguish between these two criminal concepts and the broader concept of civil personal jurisdiction. Plenty of foreign nationals get sued in the U.S. for a variety of activities. Whether they are subject to personal jurisdiction depends on a series of factors. See http://www.wisbar.org/AM/Template.cfm?Section=Wisconsin_Lawyer&template=/CM/ContentDisplay.cfm&contentid=49218

Allthough Im not a legal expert.
Sex tourism laws doesnt sound applicable in this hypotethical situation.

See, e.g., http://www.uniset.ca/other/css/877FSupp1.html for an example of a court refusing to enforce such a judgment on public policy grounds.

Actually, it’s a bit more complicated than that. See, http://boards.straightdope.com/sdmb/showpost.php?p=7941823&postcount=9