I think it depends on the wicking medium and how much is used. With cotton, I find letting it sit for 15 minutes or so lets the juice saturate the cotton. With Rayon, a few minutes and it's ready to go.
With my walgreens cotton if I don't let it sit at least an hour then it dry hit pretttty bad. Also never been able to pull off a rayon wick that didn;t dry burn something fierce.