First - and this is important - the truss rod is not used to set the action. The bridge saddles are raised and lowered to adjust the action. That said, there is some interaction between the neck tension and action, but don't try to adjust your action with the truss rod alone.
Second - your action is 1/4" after having it professionally set up? That is high, and it shouldn't be the jazz neck's fault. I would take it back and tell them that is unacceptable (unless you like it that way).
My best advice to you is to go to the fender site and read about setups. Then see if you feel comfortable doing it yourself. Everyone should be able to do their own.
BTW: Fender specs are for the 7th fret, and depend on the neck radius. They also depend on whether you are looking at the bass or treble side of the neck. In general, their setups are for 3/32" on bass and 5/64" on treble. Also, make sure you are measuring correctly - to the bottom of the string (closest to the fretboard), not to the top.
Here's the link:
http://www.fender.com/support/basses.php