You can emphasize the jig notes several ways, obviously tonguing, but doing so on every bar would be overkill. Also by glottal stop, which is softer than tonguing, where you close your throat for a moment so you have a slight burst of air to emphasize. Also by a cut between bars really pops out a note.
Mostly, with wind instruments, though, you lengthen the note. Just a little. Not nearly enough to warrant changing its timing value in the sheet music. String instrument players will say, “No, you just play louder, not longer.” They’re wrong. On the whistle, that’s nearly impossible to do without changing pitch. (With the flute, you can adjust embouchure at the same time, so it’s a bit more reasonable to attempt.)
Also, be sure your timing is absolutely hard onto the lead note in the bar. The other notes might slosh a little, especially as you squeeze ornaments in, but that lead note comes in strong just exactly when your foot/the dancer’s feet/the metronome click comes down.
The best way to get the feel for the subtlety of timing is to play with others, the next best is to play along with recorded music, but you really want to start at slower than full speed. If you don’t have good timing at a slow speed, it’ll fall apart at a high speed.
The most important factor, though, really, is to feel the rhythm inside you when you play. Nobody is thinking about subtle tricks of timing when they’re playing along full tilt at the
local session, they’re just feeling the music. So play with the technical possibilities and know your instrument, but try to get the feeling. If you know how it feels, and you know what your instrument is capable of, you can express the feeling through your instrument.
And good luck. 
–Chris