It is all about sequence and feeling.
1. One needs speed so don't pinch and then tack
2. With "ready, helm
to lee" (meaning the moment we never say much more than let's go...) let go a bit of the jib sheet so that the main force is out of the sail. Not completely loose because it will mess up.
3. Depending on the speed of turning you can decide to pull in the sheet when you are in the wind to backwind the jib a bit and give the bow a push as it were (my school
was dutch sailing barges that needed significant backwinding to even be able to turn, with a keel yacht it is much easier but this is a neat trick also when you fear you are stalling)
4. When you see that you are through the "dead point" of the tack move the jib over if you do this well timed you won't even need the winch