I sometimes have that "jump" problem with both nylon and wound strings, despite smoothing and lubrication of the nut. I find it helps to start tuning low and raise the pitch--e.g., lowering a sharp string below correct pitch and raising it to "in tune." Also, for fine tuning I sometimes give a sticky string a little help by lifting it a little at midpoint to stretch it over the nut; or, needing to go sharp a tiny bit, I might apply a little pressure behind the nut to help the string over it.
Regards, Leonard Williams [] (_) ~